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 Chok, James T., author.
 London, United Kingdom : Academic Press, an imprint of Elsevier, [2020].
 Description
 Book — 1 online resource.
2. Real and functional analysis [2020]
 Bogachev, V. I. (Vladimir Igorevich), 1961
 Cham : Springer, 2020.
 Description
 Book — 1 online resource (xvi, 586 pages)
 Summary

 Metric and Topological Spaces. Fundamentals of Measure Theory. The Lebesgue Integral. Connections between the Integral and Derivative. Normed and Euclidean Spaces. Linear Operators and Functionals. Spectral Theory. Locally Convex Spaces and Distributions. The Fourier Transform and Sobolev Spaces. Unbounded Operators and Operator Semigroups. Banach Algebras. InfiniteDimensional Analysis.
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 Moroșanu, Gheorghe.
 Cham : Springer, c2019.
 Description
 Book — 1 online resource (439 p.).
 Summary

 1. Introduction.
 2. Metric Spaces.
 3. The Lebesgue Integral and Lp Spaces.
 4. Continuous Linear Operators and Functionals.
 5. Distributions, Sobolev Spaces.
 6. Hilbert Spaces.
 7. Adjoint, Symmetric and Selfadjoint Linear Operators.
 8. Eigenvalues and Eigenvectors.
 9. Semigroups of Linear Operators.
 10. Solving Linear Evolution Equations by the Fourier Method.
 11. Integral Equations.
 12. Answers to Exercises. Bibliography.
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4. Introduction to functional data analysis [2017]
 Kokoszka, P. (Piotr), author.
 Boca Raton, FL : CRC Press, [2017]
 Description
 Book — 1 online resource.
 Summary

 First steps in the analysis of functional data Basis expansions Sample mean and covariance Principal component functions Analysis of BOA stock returns Diffusion tensor imaging Problems Further topics in exploratory FDA Derivatives Penalized smoothing Curve alignment Further reading Problems Mathematical framework for functional data Square integrable functions Random functions Linear transformations Scalar on  function regression Examples Review of standard regression theory Difficulties specific to functional regression Estimation through a basis expansion Estimation with a roughness penalty Regression on functional principal components Implementation in the refund package Nonlinear scalaronfunction regression Problems Functional response models Least squares estimation and application to angular motion Penalized least squares estimation Functional regressors Penalized estimation in the refund package Estimation based on functional principal components Test of no effect Verification of the validity of a functional linear model Extensions and further reading Problems Functional generalized linear models Background Scalaronfunction GLM's Functional response GLM Implementation in the refund package Application to DTI Further reading Problems Sparse FDA Introduction Mean function estimation Covariance function estimation Sparse functional PCA Sparse functional regression Problems Functional time series Fundamental concepts of time series analysis Functional autoregressive process Forecasting with the HyndmanUllah method Forecasting with multivariate predictors Longrun covariance function Testing stationarity of functional time series Generation and estimation of the FAR(1) model using package fda Conditions for the existence of the FAR(1) process Further reading and other topics Problems Spatial functional data and models Fundamental concepts of spatial statistics Functional spatial fields Functional kriging Mean function estimation Implementation in the R package geofd Other topics and further reading Problems Elements of Hilbert space theory Hilbert space Projections and orthonormal sets Linear operators Basics of spectral theory Tensors Problems Random functions Random elements in metric spaces Expectation and covariance in a Hilbert space Gaussian functions and limit theorems Functional principal components Problems Inference from a random sample Consistency of sample mean and covariance functions Estimated functional principal components Asymptotic normality Hypothesis testing about the mean Confidence bands for the mean Application to BOA cumulative returns Proof of Theorem Problems.
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5. Exercises in analysis. Part 1 [2014]
 Gasiński, Leszek, author.
 Cham : Springer, 2014.
 Description
 Book — 1 online resource (x, 1037 pages) : illustrations (some color). Digital: text file; PDF.
 Summary

 1. Metric Spaces
 2. Topological Spaces
 3. Measure, Integral, and Martingales
 4. Measures and Topology
 5. Functional Analysis
 Other Problem Books
 List of Symbols
 Index.
 Çobzas, Ştefan.
 New York : Springer, 2013.
 Description
 Book — 1 online resource (x, 219 pages)
 Summary

 Introduction.1. Quasimetric and Quasiuniform Spaces. 1.1. Topological properties of quasimetric and quasiuniform spaces
 1.2. Completeness and compactness in quasimetric and quasiuniform spaces.2. Asymmetric Functional Analysis
 2.1. Continuous linear operators between asymmetric normed spaces
 2.2. HahnBanach type theorems and the separation of convex sets
 2.3. The fundamental principles
 2.4. Weak topologies
 2.5. Applications to best approximation
 2.6. Spaces of semiLipschitz functions
 Bibliography
 Index.
7. Functional calculi [electronic resource] [2013]
 Bosch Giral, Carlos.
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2013.
 Description
 Book — x, 216 p.
 Summary

 Vector and Operator Valued Measures Functions of a Self Adjoint Operator Functions of Several Commuting Self Adjoint Operators The Spectral Theorem for Normal Operators Integrating Vector Valued Functions An Abstract Functional Calculus The Riesz Operational Calculus Weyl's Functional Calculus Appendices: The Orlicz  Pettis Theorem The Spectrum of an Operator Self Adjoint, Normal and Unitary Operators Sesquilinear Functionals Tempered Distributions and the Fourier Transform.
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8. A guide to functional analysis [2013]
 Krantz, Steven G. (Steven George), 1951 author.
 Washington, DC : The Mathematical Association of America, [2013]
 Description
 Book — xii, 137 pages : illustrations ; 24 cm.
 Summary

 Preface
 1. Fundamentals
 2. Ode to the dual space
 3. Hilbert space
 4. The algebra of operators
 5. Banach algebra basics
 6. Topological vector spaces
 7. Distributions
 8. Spectral theory
 9. Convexity
 10. Fixedpoint theorems Table of notation Glossary Bibliography Index.
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9. Applied functional analysis [2010]
 Oden, J. Tinsley (John Tinsley), 1936
 2nd ed.  Boca Raton, FL : CRC Press, c2010.
 Description
 Book — xvii, 578 p. : ill. ; 27 cm.
 Summary

 Preliminaries Elementary Logic and Set Theory Relations Functions Cardinality of Sets Foundations of Abstract Algebra Elementary Topology in Rn Elements of Differential and Integral Calculus Linear Algebra Vector SpacesThe Basic Concepts Linear Transformations Algebraic Duals Euclidean Spaces Lebesgue Measure and Integration Lebesgue Measure Lebesgue Integration Theory Topological and Metric Spaces Elementary Topology Theory of Metric Spaces Banach Spaces Topological Vector Spaces HahnBanach Extension Theorem Bounded (Continuous) Linear Operators on Normed Spaces Closed Operators Topological Duals. Weak Compactness Closed Range Theorem. Solvability of Linear Equations Hilbert Spaces Basic Theory Duality in Hilbert Spaces Elements of Spectral Theory References.
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10. Elementary functional analysis [2009]
 MacCluer, Barbara D.
 New York : Springer, 2009.
 Description
 Book — x, 207 p. : ill. ; 25 cm.
 Summary

 Preface. Hilbert Space Preliminaries. Operator Theory Basics. The Big Three. Compact Operators. Banach and C+ Algebras. The Spectral Theorem. Real Analysis Topics. References. Index.
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11. Elementary functional analysis [2009]
 Swartz, Charles, 1938
 New Jersey : World Scientific, c2009.
 Description
 Book — ix, 181 p. ; 24 cm.
 Summary

 Normed Linear and Banach Spaces Linear Operators Quotient Spaces Finite Dimensional Normed Spaces Inner Product and Hilbert Spaces The HahnBanach Theorem Applications of the HahnBanach Theorem to Normed Spaces The Uniform Boundedness Principle Weak Convergence The Open Mapping and Closed Graph Theorems Projections Schauder Basis Transpose and Adjoints of Continuous Linear Operators Compact Operators The Fredholm Alternative The Spectrum of an Operator Subdivisions of the Spectrum The Spectrum of a Compact Operator Symmetric Linear Operators The Spectral Theorem for Compact Symmetric Operators Symmetric Operators with Compact Inverse Bounded Self Adjoint Operators Orthogonal Projections Sesquilinear Functionals The Spectral Theorem for Bounded Self Adjoint Operators An Operational Calculus.
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Available to students, faculty, and staff, by special arrangement in response to COVID19. To protect our access to ETAS, the physical copy is temporarily not requestable.
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12. Notes on functional analysis [2009]
 Bhatia, Rajendra, 1952 author.
 New Delhi : Hindustan Book Agency, 2009.
 Description
 Book — 1 online resource (vi, 237 pages).
 Summary

 Lecture
 1: Banach Spaces. Lecture
 2: Dimensionality. Lecture
 3: New Banach Spaces from Old. Lecture
 4: The HahnBanach Theorem. Lecture
 5: The Uniform Boundedness Principle. Lecture
 6: The Open Mapping Theorem. Lecture
 7: Dual Spaces. Lecture
 8: Some Applications. Lecture
 9: The Weak Topology. Lecture
 10: The Second Dual and the Weak* Topology. Lecture
 11: Hilbert Spaces. Lecture
 12: Orthonormal Bases. Lecture
 13: Linear Operators. Lecture
 14: Adjoint Operators. Lecture
 15: Some Special Operators in Hilbert Space. Lecture
 16: The Resolvent and The Spectrum. Lecture
 17: Subdivision of the Spectrum. Lecture
 18: Spectra of Normal Operators. Lecture
 19: Square Roots and the Polar Decomposition. Lecture
 20: Compact Operators. Lecture
 21: The Spectrum of a Compact Operator. Lecture
 22: Compact Operators and Invariant Subspaces. Lecture
 23: Trace Ideals. Lecture
 24: The Spectral Theorem  I. Lecture
 25: The Spectral Theorem  II. Lecture
 26: The Spectral Theorem  III. Index.
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 Atkinson, Kendall E.
 3rd ed.  Dordrecht ; New York : Springer, c2009.
 Description
 Book — xvi, 625 p. : ill. ; 25 cm.
 Summary

 Linear Spaces. Linear Operators on Normed Spaces. Approximation Theory. Fourier Analysis and Wavelets. Nonlinear Equations and Their Solution by Iteration. Finite Difference Method. Sobolev Spaces. Weak Formulations of Elliptic Boundary Value Problems. The Galerkin Method and Its Variants. Finite Element Analysis. Elliptic Variational Inequalities and Their Numerical Approximations. Numerical Solution of Fredholm Integral Equations of the Second Kind. Boundary Integral Equations. Multivariable Polynomial Approximations.
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QA320 .A85 2009  Unknown 
 Cannarsa, Piermarco, 1957
 Milano : Springer, ©2008.
 Description
 Book — 1 online resource (xii, 268 pages).
 Summary

 Misura e integrazione
 Spazi di misura
 Integrazione
 Spazi L p
 Misure prodotto
 Analisi funzionale
 Spazi di Hilbert
 Spazi di Banach
 Capitoli scelti
 Funzioni a variazione limitata e funzioni assolutamente continue
 Misure con segno
 Funzioni multivoche.
 Timmermann, Thomas, author.
 Zuerich, Switzerland : European Mathematical Society Publishing House, 2008.
 Description
 Book — 1 online resource (427 pages). Digital: text file; PDF.
 Summary

This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele’s duality theory of algebraic quantum groups, and Woronowicz’s compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz’s compact quantum groups are treated in the setting of C*algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans’ and Vaes’ comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj–Skandalisduality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and nonexperts from other fields. Only basic knowledge of (multi) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, C*algebras, and von Neumann algebras.
16. Linear functional analysis [2008]
 Rynne, Bryan P., 1958
 2nd ed.  London : Springer, ©2008.
 Description
 Book — 1 online resource (x, 324 pages). Digital: text file; PDF.
 Summary

 Preliminaries. Normed Spaces. Inner Product Spaces, Hilbert Spaces. Linear Operators. Duality and the HahnBanach Theorem. Linear Operators on Hilbert Spaces. Compact Operators. Integral and Differential Equations. Solutions to Exercises. Further Reading. References. Notation Index. Index.
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 Tintarev, Kyril.
 London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., c2007.
 Description
 Book — xii, 264 p. ; 24 cm.
 Summary

 Functional Spaces and Convergence Sobolev Spaces Weak Convergence Decomposition Concentration Compactness with Euclidean Shifts Concentration Compactness with Dilations Minimax Problems Differentiable Manifolds Riemannian Manifolds and Lie Groups Sobolev Spaces on Manifolds and Subelliptic Problems Further Applications.
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QA320 .T56 2007  Available 
18. A course in functional analysis [2007]
 Conway, John B., 1939
 2nd ed.  New York : Springer, 2007.
 Description
 Book — xvi, 399 p. ; 25 cm.
 Summary

 1: Hilbert Spaces.
 2: Operators on Hilbert Space.
 3: Banach Spaces. 4:Locally Convex Spaces.
 5: Weak Topologies.
 6: Linear Operators on aBanach Space.
 7: Banach Algebras and Spectral Theory for Operators ona Banach Space.
 8: C^* Algebras.
 9: Normal Operators on Hilbert Space.10: Unbounded Operators.
 11: Fredholm Theory.
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QA320 .C658 2007  Unknown 
 Gurariy, Vladimir I.
 1870th ed.  Berlin : Springer, 2005.
 Description
 Book — 1 online resource (177 pages)
 Summary

Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
 Atkinson, Kendall E.
 2nd ed.  New York : Springer, c2005.
 Description
 Book — xviii, 576 p. : ill.
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