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• A Theory on Non-Constant Frequency Decompositions and Applications (Chen).- One-component inner functions II (Cima).- Biholomorphic Cryptosystems (Daras).- Third order fermionic and fourth order bosonic operators (Ding).- Holomorphic approximation: the legacy of Weierstrass, Runge, Oka-Weil, and Mergelyan (Fornaess).- A Potapov-type approach to a truncated matricial Stieltjes-type power moment problem (Fritzsche).- Formulas and inequalities for some special functions of a complex variable (Grinshpan).- On the means of the non-trivial zeros of the Riemann zeta function (Hassani).- Minimal kernels and compact analytic objects in complex surfaces(Mongodi).- On the automorphic group of an entire function (Peretz).- Integral representations in Complex Analysis: From classical results to recent developments (Range).- On the Riemann zeta function and Gaussian multiplicative chaos (Saksman).- Some new aspects in hypercomplex analysis (Sproessig).- Some connections of complex dynamics (De Zotti).
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The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.
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• On Equivalent Properties of Hardy-Type Integral Inequality with the General Nonhomogeneous Kernel and Parameters.- Fundamental Stabilities of Various Forms of Complex Valued Functional Equations.- Statistical summability of double sequences by the weighted mean and associated approximation results.- A survey on a conjecture of rainer bruck.- Nonlinear Magneto-Elasticity: Direct and Inverse Problems.- Note on periodic and asymptotically periodic solutions of fractional differential equations.- Mathematics of Wavefields.- A Variational Technique to the Homogenization of Maxwell Equations.- The Narimanov-Moiseev multimodal analysis of nonlinear sloshing in circular conical tanks.- The Lengyel-Epstein Reaction Diffusion System.- Prediction and Control of Buckling: The Inverse Bifurcation Problems for von Karman equations.- Numerical Solution with special layer adapted meshes for singularly perturbed boundary value problems.- Use of Galerkin technique in some water wave scattering problems involving plane vertical barriers.- Dynamics of a class of Leslie-Gower predation models with a non-differentiable functional response.- Entire solutions of a nonlinear diffusion system.- Goal Programming Models for Managerial Strategic Decision Making.- Modeling highly random dynamical infectious systems.- On weighted convergence of double singular integral operators involving summation.- Circular-like and circular elements in free product banach -algebras induced by p-adic number fields Qp over primes p.- On Statistical Deferred Weighted B-convergence.- Multi Poly-Bernoulli and Multi Poly-Euler Polynomials.- Geometric properties of normalized Wright functions .- On the spectra of difference operators over some Banach spaces.
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This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications.
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• 1 Introduction.- 2 Real Numbers.- 3 Sequences and Series.- 4 Functions and Continuity.- 5 Derivatives and Differentiation.- 6 Integrals and Integration.- 7 The Elementary Transcendental Functions.- 8 The Techniques of Integration.- 9 Complex Numbers.- 10 Complex Sequences and Series.- 11 Function Sequences and Function Series.- 12 Improper Integrals.- Index.
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This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout.Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of , Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
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• Examining Sets and Relations.- Investigating Basic Properties of Functions.- Defining Distance in Sets.- Using Mathematical Induction.- Investigating Convergence of Sequences and Looking for Their Limits.- Dealing with Open, Closed and Compact Sets.- Finding Limits of Functions.- Examining Continuity and Uniform Continuity of Functions.- Finding Derivatives of Functions.- Using Derivatives to Study Certain Properties of Functions.- Dealing with Higher Derivatives and Taylor's Formula.- Looking for Extremes and Examine Functions.- Investigating the Convergence of Series.- Finding Indefinite Integrals.- Investigating the Convergence of Sequences and Series of Functions.
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This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author's years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
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• Exploring the Riemann and Definite Integral.- Examining Improper Integrals.- Applying One-Dimensional Integrals to Geometry and Physics.- Dealing with Functions of Several Variables.- Investigating Derivatives of Multivariable Functions.- Examining Higher Derivatives, Differential Expressions and the Taylor's Formula.- Examining Extremes and Other Important Points.- Examining Implicit and Inverse Functions.- Solving Differential Equations of the First Order.- Solving Differential Equations of Higher Orders.- Solving Systems of First-Order Differential Equations.- Integrating in Many Dimensions.- Applying Multidimensional Integrals to Geometry and Physics.
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This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author's years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
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• Examining Curves and Surfaces.- Investigating Conditional Extremes.- Investigating Integrals with Parameters.- Examining Unoriented Curvilinear Integrals.- Examining Differential Forms.- Examining Oriented Curvilinear Integrals.- Studying Functions of Complex Variable.- Investigating Singularities of Complex Functions.- Dealing with Multi-Valued Functions.- Studying Fourier Series.
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This textbook offers an extensive list of completely solved problems in mathematical analysis. This third of three volumes covers curves and surfaces, conditional extremes, curvilinear integrals, complex functions, singularities and Fourier series. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author's years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.
(source: Nielsen Book Data)

• FM.- Frictional Contact Problems for Steady Flow of Incompressible Fluids in Orlicz Spaces.- Discrete Fourier Transform and Theta Function Identities.- On Some Combinatorics of Rogers-Ramanujan Type Identities Using Signed Color Partitions.- Piecewise Continuous Stepanov-Like Almost Automorphic Functions with Applications to Impulsive Systems.- On the Convergence of Secant-Like Methods.- Spacetimes as Topological Spaces, and the Need to Take Methods of General Topology More Seriously.- Analysis of Generalized BBM Equations: Symmetry Groups and Conservation Laws.- Symmetry Analysis and Conservation Laws for Some Boussinesq Equations with Damping Terms.- On Some Variable Exponent Problems with No-Flux Boundary Condition.- On the General Decay for a System of Viscoelastic Wave Equations.- Mathematical Theory of Incompressible Flows: Local Existence, Uniqueness, and Blow-Up of Solutions in Sobolev-Gevrey Spaces.- Mathematical Research for Models Which is Related to Chemotaxis System.- Optimal Control of Quasivariational Inequalities with Applications to Contact Mechanics.- On Generalized Derivative Sampling Series Expansion.- Voronoi Polygonal Hybrid Finite Elements and Their Applications.- VariationalMethods for Schroedinger Type Equations.- Nonlinear Nonhomogeneous Elliptic Problems.- Summability of Double Sequences and Double Series Over Non-Archimedean Fields: A Survey.- On Approximate Solutions of Linear and Nonlinear Singular Integral Equations.- On Approximate Solutions of Linear and Nonlinear Singular Integral Equations.- On Difference Double Sequences and Their Applications.- Pointwise Convergence Analysis for Nonlinear Double m-Singular Integral Operators.- A Survey on p-Adic Integrals.- On Statistical Deferred Cesaro Summability.
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This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers' understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book's main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.
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• Preliminaries
• Metric and Normed Spaces
• Metric Spaces
• Convergence and Completeness
• Topology in Metric Spaces
• Compact Sets in Metric Spaces
• Continuity for Functions on Metric Spaces
• Normed Spaces
• Vector Spaces
• Seminorms and Norms
• Infinite Series in Normed Spaces
• Equivalent Norms
• The Uniform Norm
• Some Function Spaces
• Holder and Lipschitz Continuity
• Lebesgue Measure
• Exterior Lebesgue Measure
• Boxes
• Some Facts about Boxes
• Exterior Lebesgue Measure
• The Exterior Measure of a Box
• The Cantor Set
• Regularity of Exterior Measure
• Lebesgue Measure
• Definition and Basic Properties
• Toward Countable Additivity and Closure under Complements
• Countable Additivity
• Equivalent Formulations of Measurability
• Carathéodory's Criterion
• Almost Everywhere and the Essential Supremum
• More Properties of Lebesgue Measure
• Continuity from Above and Below
• Cartesian Products
• Linear Changes of Variable
• Nonmeasurable Sets
• The Axiom of Choice
• Existence of a Nonmeasurable Set
• Further Results
• Measurable Functions
• Definition and Properties of Measurable Functions
• Extended Real-Valued Functions
• Complex-Valued Functions
• Operations on Functions
• Sums and Products
• Compositions
• Suprema and Limits
• Simple Functions
• The Lebesgue Space L...(E)
• Convergence and Completeness in L...(E)
• Egorov's Theorem
• Convergence in Measure
• Luzin's Theorem
• The Lebesgue Integral
• The Lebesgue Integral of Nonnegative Functions
• Integration of Nonnegative Simple Functions
• Integration of Nonnegative Functions
• The Monotone Convergence Theorem and Fatou's Lemma
• The Monotone Convergence Theorem
• Fatou's Lemma
• The Lebesgue Integral of Measurable Functions
• Extended Real-Valued Functions
• Complex-Valued Functions
• Properties of the Integral
• Integrable Functions and L1(E)
• The Lebesgue Space L1(E)
• Convergence in L1-Norm
• Linearity of the Integral for Integrable Functions
• Inclusions between L1(E) and L...(E)
• The Dominated Convergence Theorem
• The Dominated Convergence Theorem
• First Applications of the DCT
• Approximation by Continuous Functions
• Approximation by Really Simple Functions
• Relation to the Riemann Integral
• Repeated Integration
• Fubini's Theorem
• Tonelli's Theorem
• Convolution
• Differentiation
• The Cantor-Lebesgue Function
• Functions of Bounded Variation
• Definition and Examples
• Lipschitz and Holder Continuous Functions
• Indefinite Integrals and Antiderivatives
• The Jordan Decomposition
• Covering Lemmas
• The Simple Vitali Lemma
• The Vitali Covering Lemma
• Differentiability of Monotone Functions
• The Lebesgue Differentiation Theorem
• L1-Convergence of Averages
• Locally Integrable Functions
• The Maximal Theorem
• The Lebesgue Differentiation Theorem
• Lebesgue Points
• Absolute Continuity and the Fundamental Theorem of Calculus
• Absolutely Continuous Functions
• Differentiability of Absolutely Continuous Functions
• Growth Lemmas
• The Banach-Zaretsky Theorem
• The Fundamental Theorem of Calculus
• Applications of the FTC
• Integration by Parts
• The Chain Rule and Changes of Variable
• Convex Functions and Jensen's Inequality
• The lp Spaces
• The lp Spaces
• Hölder's Inequality
• Minkowski's Inequality
• Convergence in the lp Spaces
• Completeness of the lp Spaces
• lp for p < 1
• C0 and C00
• The Lebesgue Space Lp(E)
• Seminorm Properties of II : IIp
• Identifying Functions That Are Equal Almost Everywhere
• Lp(E) for 0 < p < 1
• The Converse of Hölder's Inequality
• Convergence in Ip-norm
• Dense Subsets of Lp(E)
• Separability of Lp(E)
• Hilbert Spaces and L2(E)
• Inner Products and Hilbert Spaces
• The Definition of an Inner Product
• Properties of an Inner Product
• Hilbert Spaces
• Orthogonality
• Orthogonal Complements
• Orthogonal Projections
• Characterizations of the Orthogonal Projection
• The Closed Span
• The Complement of the Complement
• Complete Sequences
• Orthonormal Sequences and Orthonormal Bases
• Orthonormal Sequences
• Unconditional Convergence
• Orthogonal Projections Revisited
• Orthonormal Bases
• Existence of an Orthonormal Basis
• The Legendre Polynomials
• The Haar System
• Unitary Operators
• The Trigonometric System
• Convolution and the Fourier Transform
• Convolution
• The Definition of Convolution
• Existence
• Convolution as Averaging
• Approximate Identities
• Young's Inequality
• The Fourier Transform
• The Inversion Formula
• Smoothness and Decay
• Fourier Series
• Periodic Functions
• Decay of Fourier Coefficients
• Convolution of Periodic Functions
• Approximate Identities and the Inversion Formula
• Completeness of the Trigonometric System
• Convergence of Fourier Series for p ... 2
• The Fourier Transform on L2(R)
• Hints for Selected Exercises and Problems
• Index of Symbols
• References
• Index.

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author's lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.
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• Exact solution to systems of linear first-order integro-differential equations with multipoint and integral conditions (Baiburin and Providas).- A variational approach to the financial problem with insolvencies and analysis of the contagion (Daniele et al.).- Local Fixed Point Theorems in Generalized B-Metric Spaces (Czerwik and Jozwik).- Inequalities and Approximations for the Finite Hilbert Transform: a Survey of Recent Results (Dragomir).- On hyperstability of the two-variable Jensen functional equation on restricted domain (EL-Fassi).- On the Study of Circuit Chains Associated with a Random Walk with Jumps in Fixed, Random Environments: Criteria of Recurrence and Transience (Ganatsiou).- On selections of some generalized set-valued inclusions (Rassias et al.).- Certain fractional integral and differential formulas involving the extended incomplete generalized hypergeometric function (Agarwal et al.).- On the stability of the triangular equilibrium points in the elliptic restricted three-body problem with radiation and oblateness (Kalantonis et al.).- Some different type integral inequalities and their applications (Kashuri and Liko).- Extensions of Kannappan's and Van Vleck's functional equations on semigroups (Elhoucien et al.).- Recent Advances of Convexity Theory and its Inequalities (Jichang).- Additive functional inequalities and partial multipliers in complex Banach algebras (Lee et al.).- Additive -functional inequalities and their applications (Park et al.).- Graphic contraction principle and applications (Petrusel and Rus).- A new approach for the inversion of the attenuated Radon transform (Protonotarios et al.).- On algorithms for difference of monotone operators (Cattani et al.).- Finite Element Analysis in Fluid Mechanics (Xenos et al.).- On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function (Rassias and Yang).- On metric structures of normed gyrogroups (Suksumran).- Birelator spaces are natural generalizations of not only bitopological spaces, but also ideal topological spaces (Szaz).- PPF dependent fixed points in Razumikhin metrical chains (Turinici).- Equivalent Properties of Parameterized Hilbert-Type Integral Inequalities (Yang).- Trotter product formula for non-self-adjoint Gibbs semigroups (Zagrebnov).
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An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics. .
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• FM.- Ben de Pagter: Curriculum Vitae .- 2-Local automorphisms on AW*-algebras.- Orthosymmetric Archimedean-valued vector lattices.- Arens extensions for polynomials and the Woodbury-Schep formula.- On the endpoints of De Leeuw restriction theorems.- Lebesgue topologies and mixed topologies.- Lattice homomorphisms in harmonic analysis.- Noncommutative Boyd interpolation theorems revisited.- Strict singularity: a lattice approach.- Asymptotics of operator semigroups via the semigroup at infinity.- Markov processes, strong Markov processes and Brownian motion in Riesz spaces.- A solution to the Al-Salam-Chihara moment problem.- The Katowice problem for analysts.- Onefold and twofold Ellis-Gohberg inverse problems for scalar Wiener class functions.- Relatively uniform convergence in partially ordered vector spaces revisited.- Dedekind complete and order continuous Banach C(K)-modules.- Matrix valued Laguerre polynomials.- Weighted Noncommutative Banach Function Spaces.- Majorization for compact and weakly compact polynomials on Banach lattices.- The UMD property for Musielak-Orlicz spaces.- The ls -Boundedness of a Family of Integral Operators on UMD Banach Function Spaces.- Backward stochastic evolution equations in UMD Banach spaces.- On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics.- Classes of localizable measure spaces.- A residue formula for locally compact noncommutative manifolds.- Regular states and the Regular Algebra Numerical Range.- Bilaplace Eigenfunctions compared with Laplace Eigenfunctions in some special cases.-Representations of the Dedekind completions of spaces of continuous functions.- Joint representation of a Riesz space and its conjugate space.- When do the regular operators between two Banach lattices form a lattice?.- Lexicographic cones and the ordered projective tensor product.
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Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Gluck, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernandez, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lu, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Roman, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.
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• FM.- Ben de Pagter: Curriculum Vitae .- 2-Local automorphisms on AW*-algebras.- Orthosymmetric Archimedean-valued vector lattices.- Arens extensions for polynomials and the Woodbury-Schep formula.- On the endpoints of De Leeuw restriction theorems.- Lebesgue topologies and mixed topologies.- Lattice homomorphisms in harmonic analysis.- Noncommutative Boyd interpolation theorems revisited.- Strict singularity: a lattice approach.- Asymptotics of operator semigroups via the semigroup at infinity.- Markov processes, strong Markov processes and Brownian motion in Riesz spaces.- A solution to the Al-Salam-Chihara moment problem.- The Katowice problem for analysts.- Onefold and twofold Ellis-Gohberg inverse problems for scalar Wiener class functions.- Relatively uniform convergence in partially ordered vector spaces revisited.- Dedekind complete and order continuous Banach C(K)-modules.- Matrix valued Laguerre polynomials.- Weighted Noncommutative Banach Function Spaces.- Majorization for compact and weakly compact polynomials on Banach lattices.- The UMD property for Musielak-Orlicz spaces.- The ls -Boundedness of a Family of Integral Operators on UMD Banach Function Spaces.- Backward stochastic evolution equations in UMD Banach spaces.- On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics.- Classes of localizable measure spaces.- A residue formula for locally compact noncommutative manifolds.- Regular states and the Regular Algebra Numerical Range.- Bilaplace Eigenfunctions compared with Laplace Eigenfunctions in some special cases.-Representations of the Dedekind completions of spaces of continuous functions.- Joint representation of a Riesz space and its conjugate space.- When do the regular operators between two Banach lattices form a lattice?.- Lexicographic cones and the ordered projective tensor product.
• (source: Nielsen Book Data)

Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Gluck, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernandez, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lu, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Roman, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.
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• Part I Yingkang: Remembering Professor Yingkang Hu.- Remembrances.- On Some Properties of Moduli of Smoothness with JacobiWeights.- Part II Approximation Theory, Harmonic and Complex Analysis, Splines and Classical Fourier Theory.- Special Difference Operators and the Constants in the Classical Jackson-Type Theorems.- Comparison Theorems for Completely and Multiply Monotone Functions and Their Applications.- Concerning Exponential Bases on Multi-Rectangles of Rd.- Hankel Transforms of General Monotone Functions.- Univalence of a Certain Quartic Function.- Finding, Stabilizing, and Verifying Cycles of Nonlinear Dynamical Systems.- Finding Orbits of Functions Using Suffridge Polynomials.- The Sharp Remez-Type Inequality for Even Trigonometric Polynomials on the Period.- The Lebesgue Constants of Fourier Partial Sums.- Liouville-Weyl Derivatives of Double Trigonometric Series.- Inequalities in Approximation Theory Involving Fractional Smoothness in Lp, 0 < p < 1.- On de Boor-Fix Type Functionals for Minimal Splines.- A Multidimensional Hardy-Littlewood Theorem.- The Spurious Side of DiagonalMultipoint Pade Approximants.- Spline Summability of Cardinal Sine Series and the Bernstein Class.- Integral Identities for Polyanalytic Functions.- Pointwise Behavior of Christoffel Function on Planar Convex Domains.- Towards Best Approximations for
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Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Pade approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.
(source: Nielsen Book Data)

Here is an unsurpassed resource-important accounts of a variety of dynamic systems topicsrelated to number theory. Twelve distinguished mathematicians present a rare complete analyticsolution of a geodesic quantum problem on a negatively curved surface . and explicitdetermination of modular function growth near a real point . applications of number theoryto dynamical systems and applications of mathematical physics to number theory .tributes to the often-unheralded pioneers in the field . an examination of completely integrableand exactly solvable physical models . and much more!Classical and Quantum Models and Arithmetic Problems is certainly a major source of information, advancing the studies of number theorists, algebraists, and mathematical physicistsinterested in complex mathematical properties of quantum field theory, statistical mechanics, and dynamic systems. Moreover, the volume is a superior source of supplementary readingfor graduate-level courses in dynamic systems and application of number theory

In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and Mittag-Leffler's theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Frechet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy's Theorem and Cauchy's formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Frechet spaces of holomorphic functions The -complex The twisted -complex and Schroedinger operators.
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• 1. The real numbers--
• 2. Differentiation--
• 3. Integration--
• 4. Sequences of functions--
• 5. Metric and Euclidean spaces--
• 6. Differentiation in higher dimensions--
• 7. Integration in higher dimensions--
• 8. Curves and surfaces--
• 9. Differential forms.
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This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
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• Logic and Proof Techniques. Sets and Functions. Real Numbers. Open and Closed Sets. Cardinality. Real-valued Functions. Real Sequences. Real Sequences (Contd.). Infinite Series. Infinite Series (Contd.). Limits of Functions. Continuous Functions. Discontinuous Functions. Uniform and Absolute Continuities and Functions of Bounded Variation. Differentiable Functions. Higher Order Differentiable Functions. Convex Functions. Indeterminate Forms. Riemann Integration. Properties of the Riemann Integral. Improper Integrals. Riemann-Lebesgue Theorem. Riemann-Stieltjes Integral. Sequences of Functions. Sequences of Functions (Contd.). Series of Functions. Power and Taylor Series. Power and Taylor Series (Contd.). Metric Spaces. Metric Spaces (Contd.). Bibliography. Index.
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This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
(source: Nielsen Book Data)

• Prologue.- Measures.- Integrations.- Signed Measures and Differentiation.- Topology: A Generalization of Open Sets.- Elements of Functional Analysis.- Lp Spaces.
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This compact textbook is a collection of the author's lecture notes for a two-semester graduate-level real analysis course. While the material covered is standard, the author's approach is unique in that it combines elements from both Royden's and Folland's classic texts to provide a more concise and intuitive presentation. Illustrations, examples, and exercises are included that present Lebesgue integrals, measure theory, and topological spaces in an original and more accessible way, making difficult concepts easier for students to understand. This text can be used as a supplementary resource or for individual study.
(source: Nielsen Book Data)

• Chapter 1. Lebesgue Integration
• Chapter 2. Lp-Spaces
• Chapter 3. Fourier Transforms
• Chapter 4. Holomorphic and Harmonic Functions
• Chapter 5. Conformal Mapping
• Chapter 6. Analytic Continuation
• Chapter 7. Special Functions.

This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries.-- Provided by publisher.

• 1 Sets, functions and the real numbers.- 2 Basic properties of real numbers, sequences and continuous functions.- 3 Infinite series.- 4 Uniform convergence.- 5 Functions.-
• 6. Topics from classical analysis: The Gamma-function and the Euler-Maclaurin formula.- 7 Metric spaces.- 8 Fractals and iterated function systems.- 9 Differential calculus on Rm.- Bibliography. Index.
• (source: Nielsen Book Data)

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author's extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.
(source: Nielsen Book Data)