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1. The elements of advanced mathematics [2018]
 Krantz, Steven G. (Steven George), 1951
 Fourth edition.  Boca Raton : CRC Press, Taylor & Francis Group, [2018]
 Description
 Book — xxiii, 390 pages ; 24 cm.
 Summary

 Basic Logic. Methods of Proof. Set Theory.
 Chapter 4 Relations and Functions. Axioms of Set Theory, Paradoxes, and Rigor. Number Systems. More on the Real Number System. A Glimpse of Topology. Elementary Number Theory. ZeroKnowledge Proofs and Cryptography.
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QA37.3 .K73 2018  Available 
 Krantz, Steven G. (Steven George), 1951 author.
 Second edition.  Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — xx, 243 pages ; 26 cm
 Summary

 The basicsTopics specific to the writing of mathematicsExpositionOther types of writingBooksWriting with a computerThe world of hightech publishingClosing thoughtsBibliographyIndex.
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QA42 .K73 2017  Unknown 
 Krantz, Steven G. (Steven George), 1951 author.
 Boca Raton : CRC Press/Taylor & Francis Group, [2016]
 Description
 Book — xvi, 464 pages : illustrations ; 25 cm.
 Summary

 What Is a Differential Equation? Introductory Remarks A Taste of Ordinary Differential Equations The Nature of Solutions Separable Equations FirstOrder Linear Equations Exact Equations Orthogonal Trajectories and Families of Curves Homogeneous Equations Integrating Factors Reduction of Order The Hanging Chain and Pursuit Curves Electrical Circuits Anatomy of an Application Problems for Review and Discovery SecondOrder Linear Equations SecondOrder Linear Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters The Use of a Known Solution to Find Another Vibrations and Oscillations Newton's Law of Gravitation and Kepler's Laws HigherOrder Equations Historical Note: Euler Anatomy of an Application Problems for Review and Discovery Power Series Solutions and Special Functions Introduction and Review of Power Series Series Solutions of FirstOrder Equations SecondOrder Linear Equations: Ordinary Points Regular Singular Points More on Regular Singular Points Gauss's Hypergeometric Equation Historical Note: Gauss Historical Note: Abel Anatomy of an Application Problems for Review and Discovery Numerical Methods Introductory Remarks The Method of Euler The Error Term An Improved Euler Method The RungeKutta Method Anatomy of an Application Problems for Review and Discovery Fourier Series: Basic Concepts Fourier Coefficients Some Remarks about Convergence Even and Odd Functions: Cosine and Sine Series Fourier Series on Arbitrary Intervals Orthogonal Functions Historical Note: Riemann Anatomy of an Application Problems for Review and Discovery SturmLiouville Problems and Boundary Value Problems What Is a SturmLiouville Problem? Analyzing a SturmLiouville Problem Applications of the SturmLiouville Theory Singular SturmLiouville Anatomy of an Application Problems for Review and Discovery Partial Differential Equations and Boundary Value Problems Introduction and Historical Remarks Eigenvalues, Eigenfunctions, and the Vibrating String The Heat Equation The Dirichlet Problem for a Disc Historical Note: Fourier Historical Note: Dirichlet Problems for Review and Discovery Anatomy of an Application Laplace Transforms Introduction Applications to Differential Equations Derivatives and Integrals of Laplace Transforms Convolutions The Unit Step and Impulse Functions Historical Note: Laplace Anatomy of an Application Problems for Review and Discovery Systems of FirstOrder Equations Introductory Remarks Linear Systems Homogeneous Linear Systems with Constant Coefficients Nonlinear Systems: Volterra's PredatorPrey Equations Anatomy of an Application Problems for Review and Discovery The Nonlinear Theory Some Motivating Examples Specializing Down Types of Critical Points: Stability Critical Points and Stability for Linear Systems Stability by Liapunov's Direct Method Simple Critical Points of Nonlinear Systems Nonlinear Mechanics: Conservative Systems Periodic Solutions: The PoincareBendixson Theorem Historical Note: Poincare Anatomy of an Application Problems for Review and Discovery Appendix: Review of Linear Algebra.
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QA371 .S465 2016  Unknown 
4. Convex analysis [2015]
 Krantz, Steven G. (Steven George), 1951 author.
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xiii, 161 pages : illustrations ; 24 cm.
 Summary

 Why Convexity? Basic Ideas Introduction The Classical Theory Separation Theorems Approximation Functions Defining Function Analytic Definition Convex Functions Exhaustion Functions More on Functions Other Characterizations Convexity of Finite Order Extreme Points Support Functions Approximation from Below Bumping Applications The KreinMilman Theorem The Minkowski Sum BrunnMinkowski More Sophisticated Ideas The Polar of a Set Optimization Introductory Thoughts Setup for the Simplex Method Augmented Form The Simplex Algorithm Generalizations Integral Representation The Gamma Function Hard Analytic Facts Sums and Projections The MiniMax Theorem Concluding Remarks Appendix: Technical Tools Table of Notation Glossary.
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QA639.5 .K73 2015  Unknown 
 Krantz, Steven G. (Steven George), 1951 author.
 Second edition.  Boca Raton : CRC Press, Taylor & Francis Group, [2015]
 Description
 Book — xvi, 541 pages : illustrations ; 24 cm.
 Summary

 Preface What is a Differential Equation? Introductory Remarks The Nature of Solutions Separable Equations FirstOrder Linear Equations Exact Equations Orthogonal Trajectories and Families of Curves Homogeneous Equations Integrating Factors Reduction of Order Dependent Variable Missing Independent Variable Missing The Hanging Chain and Pursuit Curves The Hanging Chain Pursuit Curves Electrical Circuits Anatomy of an Application: The Design of a Dialysis Machine Problems for Review and Discovery SecondOrder Linear Equations SecondOrder Linear Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters The Use of a Known Solution to Find Another Vibrations and Oscillations Undamped Simple Harmonic Motion Damped Vibrations Forced Vibrations A Few Remarks about Electricity Newton's Law of Gravitation and Kepler's Laws Kepler's Second Law Kepler's First Law Kepler's Third Law Higher Order Equations Historical Note: Euler Anatomy of an Application: Bessel Functions and the Vibrating Membrane Problems for Review and Discovery Qualitative Properties and Theoretical Aspects A Bit of Theory Picard's Existence and Uniqueness Theorem The Form of a Differential Equation Picard's Iteration Technique Some Illustrative Examples Estimation of the Picard Iterates Oscillations and the Sturm Separation Theorem The Sturm Comparison Theorem Anatomy of an Application: The Green's Function Problems for Review and Discovery Power Series Solutions and Special Functions Introduction and Review of Power Series Review of Power Series Series Solutions of FirstOrder Equations SecondOrder Linear Equations: Ordinary Points Regular Singular Points More on Regular Singular Points Gauss's Hypergeometric Equation Historical Note: Gauss Historical Note: Abel Anatomy of an Application: Steady State Temperature in a Ball Problems for Review and Discovery Fourier Series: Basic Concepts Fourier Coefficients Some Remarks about Convergence Even and Odd Functions: Cosine and Sine Series Fourier Series on Arbitrary Intervals Orthogonal Functions Historical Note: Riemann Anatomy of an Application: Introduction to the Fourier Transform Problems for Review and Discovery Partial Differential Equations and Boundary Value Problems Introduction and Historical Remarks Eigenvalues, Eigenfunctions, and the Vibrating String Boundary Value Problems Derivation of the Wave Equation Solution of the Wave Equation The Heat Equation The Dirichlet Problem for a Disc The Poisson Integral SturmLiouville Problems Historical Note: Fourier Historical Note: Dirichlet Anatomy of an Application: Some Ideas from Quantum Mechanics Problems for Review and Discovery Laplace Transforms Introduction Applications to Differential Equations Derivatives and Integrals of Laplace Transforms Convolutions Abel's Mechanics Problem The Unit Step and Impulse Functions Historical Note: Laplace Anatomy of an Application: Flow Initiated by an ImpulsivelyStarted Flat Plate Problems for Review and Discovery The Calculus of Variations Introductory Remarks Euler's Equation Isoperimetric Problems and the Like Lagrange Multipliers Integral Side Conditions Finite Side Conditions Historical Note: Newton Anatomy of an Application: Hamilton's Principle and its Implications Problems for Review and Discovery Numerical Methods Introductory Remarks The Method of Euler The Error Term An Improved Euler Method The RungeKutta Method Anatomy of an Application: A Constant Perturbation Method for Linear, SecondOrder Equations Problems for Review and Discovery Systems of FirstOrder Equations Introductory Remarks Linear Systems Homogeneous Linear Systems with Constant Coefficients Nonlinear Systems: Volterra's PredatorPrey Equations Solving HigherOrder Systems Using Matrix Theory Anatomy of an Application: Solution of Systems with Matrices and Exponentials Problems for Review and Discovery The Nonlinear Theory Some Motivating Examples Specializing Down Types of Critical Points: Stability Critical Points and Stability for Linear Systems Stability by Liapunov's Direct Method Simple Critical Points of Nonlinear Systems Nonlinear Mechanics: Conservative Systems Periodic Solutions: The PoincareBendixson Theorem Historical Note: Poincare Anatomy of an Application: Mechanical Analysis of a Block on a Spring Problems for Review and Discovery Dynamical Systems Flows Dynamical Systems Stable and Unstable Fixed Points Linear Dynamics in the Plane Some Ideas from Topology Open and Closed Sets The Idea of Connectedness Closed Curves in the Plane Planar Autonomous Systems Ingredients of the Proof of PoincareBendixson Anatomy of an Application: Lagrange's Equations Problems for Review and Discovery Appendix on Linear Algebra Vector Spaces The Concept of Linear Independence Bases Inner Product Spaces Linear Transformations and Matrices Eigenvalues and Eigenvectors Bibliography.
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QA371 .K636 2015  Unknown 
6. How to teach mathematics [2015]
 Krantz, Steven G. (Steven George), 1951 author.
 Third edition.  Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — xx, 146 pages ; 26 cm
 Summary

 * Guiding principles* Practical matters* Spiritual matters* The electronic world* Difficult matters* A new beginning* Bibliography* Index.
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QA11 .K776 2015  Unknown 
 Krantz, Steven G. (Steven George), 1951
 New York : SpringerVerlag, c2013.
 Description
 Book — xiii, 292 p. ; 25 cm.
 Summary

 Introductory Ideas
 The Bergman Metric
 Geometric and Analytic Ideas
 Partial Differential Equations
 Further Geometric Explorations
 Additional Analytic Topics
 Curvature of the Bergman Metric
 Concluding Remarks.
 Introductory ideas
 The Bergman Kernel
 Calculating the Bergman Kernel
 The PoincaréBergman distance on the disc
 Construction of the Bergman Kernel by way of differential equations
 Construction of the Bergman Kernel by way of conformal invariance
 The Szegő and PoissonSzegő Kernels
 Formal ideas of Aronszajn
 A new Bergman basis
 Further examples
 A real Bergman space
 The behavior of the singularity in a general setting
 The annulus
 A direct connection between the Bergman and Szegő Kernels
 Introduction
 The case of the disc
 The unit ball in Cn
 Strongly pseudoconvex domains
 Concluding remarks
 Multiply connected domains
 The Bergman Kernel for a Sobolev space
 Ramadanov's theorem
 Coda on the Szegő Kernel
 Boundary localization
 Definitions and notation
 A representative result
 The more general result in the plane
 Domains in higherdimensional complex space
 Exercises
 The Bergman metric
 Smoothness to the boundary of biholomorphic mappings
 Boundary behavior of the Bergman metrie
 The biholomorphic inequivalence of the ball and the polydisc exercises
 Further geometrie and analytic theory
 Bergman representative coordinates
 The Berezin transform
 Preliminary remarks
 Introduction to the PoissonBergman Kernel
 Boundary behavior
 Ideas of Fefferman
 Results on the invariant laplacian
 The Dirichlet problem for the invariant laplacian on the ball
 Concluding remarks
 Exercises
 Partial differential equations
 The idea of spherical harmonics
 Advanced topics in the theory of spherical harmonics : the zonal harmonics
 Spherical harmonics in the complex domain and applications
 An application to the Bergman projection
 Exercises
 Further geometric explorations
 Introductory remarks
 Semicontinuity of automorphism groups
 Convergence of holomorphic mappings
 Finite type in dimension two
 The semicontinuity theorem
 Some examples
 Further remarks
 The Lu QiKeng conjecture
 The Lu QiKeng theorem
 The dimension of the Bergman space
 The Bergman theory on a manifold
 Kernel forms
 The invariant metric
 Boundary behavior of the Bergman metric
 Exercises
 Additional analytic topics
 The DiederichFornæss worm domain
 More on the worm
 Nonsmooth versions of the worm domain
 Irregularity of the Bergman projection
 Irregularity properties of the Bergman Kernel
 The Kohn projection formula
 Boundary behavior of the Bergman Kernel
 Hörmander's result on boundary behavior
 The Fefferman's asymptotic expansion
 The Bergman Kernel for a Sobolev space
 Regularity of the dirichlet problem on a smoothly bounded domain and conformal mapping
 Existence of certain smooth plurisubharmonic defining functions for strictly pseudoconvex domains and applications
 Introduction
 Proof of theorem 6.10.1
 Application of the complex mongeampère equation
 An example of David Barrett
 The Bergman Kernel as a Hilbert integral
 Exercises
 Curvature of the Bergman metric
 What is the scaling method?
 Higher dimensional scaling
 Nonisotropic scaling
 Normal convergence of sets
 Localization
 Klembeck's theorem with C2stability
 The main goal
 The Bergman metric near strictly pseudoconvex boundary points
 Exercises
 Concluding remarks
 Table of notation
 Bibliography
 Index.
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QA331 .K73 2013  Unknown 
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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QA320 .K668 2013  Unknown 
9. A mathematician comes of age [2012]
 Krantz, Steven G. (Steven George), 1951
 Washington, DC : Mathematical Association of America, c2012.
 Description
 Book — xvii, 137 p. : ill ; 24 cm.
 Summary

 Preface
 1. Introductory thoughts
 2. Math concepts
 3. Teaching techniques
 4. Social issues
 5. Cognitive issues
 6. What is a mathematician?
 7. Maturity for everyone The tree of mathematical maturity Etymology of the word 'maturity' Bibliography Index.
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QA11.2 .K68 2012  Unknown 
10. The geometry of complex domains [2011]
 Greene, Robert Everist, 1943
 [Boston, Mass.] : Birkhäuser, c2011.
 Description
 Book — xiv, 303 p. : ill. ; 25 cm.
 Summary

 Preface.
 1 Preliminaries.
 2 Riemann Surfaces and Covering Spaces.
 3 The Bergman Kernel and Metric.
 4 Applications of Bergman Geometry.
 5 Lie Groups Realized as Automorphism Groups.
 6 The Significance of Large Isotropy Groups.
 7 Some Other Invariant Metrics.
 8 Automorphism Groups and Classification of Reinhardt Domains.
 9 The Scaling Method, I.
 10 The Scaling Method, II.
 11 Afterword. Bibliography. Index.
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QA608 .G74 2011  Unknown 
 Krantz, Steven G. (Steven George), 1951
 New York ; London : Springer, c2011.
 Description
 Book — xvi, 264 p. : ill. (some col.) ; 27 cm.
 Summary

 1. What is a Proof and Why?.
 2. The Ancients.
 3. The Middle Ages and Calculation.
 4. The Dawn of the Modern Age.
 5. Hilbert and the Twentieth Century.
 6. The FourColor Theorem.
 7. ComputerGenerated Proofs.
 8. The Computer as a Mathematical Aid.
 9. Aspects of Mathematical Life.
 10. The Sociology of Mathematical Proof.
 11. A Legacy of Elusive Proofs.
 12. John Horgan and "The Death of Proof".
 13. Closing Thoughts. Index of Names. References. Index.
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 Krantz, Steven G. (Steven George), 1951
 [Washington, DC] : Mathematical Association of America, c2010.
 Description
 Book — xiii, 381 p. : ill. ; 27 cm.
 Summary

 Preface
 1. The Ancient Greeks
 2. Zeno's Paradox and the concept of limit
 3. The mystical mathematics of Hypatia
 4. The Islamic world and the development of algebra
 5. Cardano, Abel, Galois, and the solving of equations
 6. Rene Descartes and the idea of coordinates
 7. The invention of differential calculus
 8. The great Isaac Newton
 9. Complex numbers and polynomials
 10. The prince of mathematics
 11. Sophie Germain and Fermat's Problem
 12. Cauchy and the foundations of analysis
 13. The prime numbers
 14. Dirichlet and how to count
 15. Riemann and the geometry of surfaces
 16. Georg Cantor and the orders of infinity
 17. The natural numbers
 18. Henri Poincare, child phenomenon
 19. Sonya Kovalevskaya and mechanics
 20. Emmy Noether and algebra
 21. Methods of proof
 22. Alan Turing and cryptography Bibliography Index.
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 Krantz, Steven G. (Steven George), 1951
 Boston : Birkhäuser, c2009.
 Description
 Book — xiv, 360 p. : ill. ; 24 cm.
 Summary

 Ontology and History of Real Analysis. The Central Idea: The Hilbert Transform. Essentials of the Fourier Transform. Fractional and Singular Integrals. A Crash Course in Several Complex Variables. Pseudoconvexity and Domains of Holomorphy. Canonical Complex Integral Operators. Hardy Spaces Old and New. to the Heisenberg Group. Analysis on the Heisenberg Group. A Coda on Domains of Finite Type.
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QA403 .K629 2009  Unknown 
14. A guide to real variables [2009]
 Krantz, Steven G. (Steven George), 1951
 [Washington, D.C.] : Mathematical Association of America, c2009.
 Description
 Book — xvi, 147 p. : ill. ; 24 cm.
 Summary

 Preface
 1. Basics
 2. Sequences
 3. Series
 4. The topology of the real line
 5. Limits and the continuity of functions
 6. The derivative
 7. The integral
 8. Sequences and series of functions
 9. Advanced topics Glossary of terms from real variable theory Bibliography Index.
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QA331.5 .K68 2009  Unknown 
15. A guide to topology [2009]
 Krantz, Steven G. (Steven George), 1951
 [Washington, D.C.] : Mathematical Association of America, c2009.
 Description
 Book — xii, 107 p. : ill. ; 24 cm.
 Summary

 Preface Part I. Fundamentals: 1.1. What is topology? 1.2. First definitions 1.3 Mappings 1.4. The separation axioms 1.5. Compactness 1.6. Homeomorphisms 1.7. Connectedness 1.8. Pathconnectedness 1.9. Continua 1.10. Totally disconnected spaces 1.11. The Cantor set 1.12. Metric spaces 1.13. Metrizability 1.14. Baire's theorem 1.15. Lebesgue's lemma and Lebesgue numbers Part II. Advanced Properties: 2.1 Basis and subbasis 2.2. Product spaces 2.3. Relative topology 2.4. First countable and second countable 2.5. Compactifications 2.6. Quotient topologies 2.7. Uniformities 2.8. Morse theory 2.9. Proper mappings 2.10. Paracompactness Part III. MooreSmith Convergence and Nets: 3.1. Introductory remarks 3.2. Nets Part IV. Function Spaces: 4.1. Preliminary ideas 4.2. The topology of pointwise convergence 4.3. The compactopen topology 4.4. Uniform convergence 4.5. Equicontinuity and the AscoliArzela theorem 4.6. The Weierstrass approximation theorem Table of notation Glossary Bibliography Index.
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QA611 .K683 2009  Unknown 
16. Geometric integration theory [2008]
 Krantz, Steven G. (Steven George), 1951
 Boston : Birkhäuser, c2008.
 Description
 Book — xiii, 339 p. : ill. ; 25 cm.
 Summary

 Preface. Basics. Caratheodory's Construction and LowerDimensional Measures. Invariant Meaures and the Construction of Haar Meaure. Covering Theorems and the Differentiation of Integrals. Analytical Tools: the Area Formula, the Coarea Formula, and Poincare Inequalities. The Calculus of Differential Forms and Stokes's Theorem. Introduction to Currents. Currents and the Calculus of Variations. Regularity of MassMinimizing Currents. Appendix.References. Index of Notation. Index.
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QA312 .K73 2008  Unknown 
17. A guide to complex variables [2008]
 Krantz, Steven G. (Steven George), 1951
 [Washington, D.C.] : Mathematical Association of America, c2008.
 Description
 Book — xviii, 182 p. : ill. ; 24 cm.
 Summary

 Preface
 1. The complex plane
 2. Complex line integrals
 3. Applications of the Cauchy theory
 4. Isolated singularities and Laurent series
 5. The argument principle
 6. The geometric theory of holomorphic functions
 7. Harmonic functions
 8. Infinite series and products
 9. Analytic continuation.
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QA331.7 .K743 2008  Unknown 
 Providence, R.I. : American Mathematical Society, c2006.
 Description
 Book — xii, 145 p. : ill. ; 26 cm.
 Summary

 An anecdotal history of the Washington University Mathematics Department by S. G. Krantz Dissertation list by G. R. Jensen and S. G. Krantz History of the Mathematics faculty by G. R. Jensen and S. G. Krantz Geometry of manifolds with special holonomy: "100 years of holonomy" by R. L. Bryant Geometric harmonic analysis in high dimensions: Challenges and opportunities by R. R. Coifman An analogue of Hilbert's seventeenth problem in one complex dimension by J. P. D'Angelo Hypoelliptic second order equations that lose derivatives by J. J. Kohn Stokes' theorem and minimal surfaces by H. B. Lawson, Jr. $L^2$ estimates on twisted CauchyRiemann complexes by J. D. McNeal From wavelets to atoms by Y. Meyer The mathematics of general relativity: Problems and progress by R. Schoen Panel discussion by R. R. Coifman, A. Bonami, R. Bryant, and J. P. D'Angelo.
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QA13.5 .M8 W37 2003  Available 
19. Function theory of one complex variable [2006]
 Greene, Robert Everist, 1943
 3rd ed.  Providence, R.I. : American Mathematical Society, c2006.
 Description
 Book — xix, 504 p. : ill. ; 27 cm.
 Summary

 Fundamental concepts Complex line integrals Applications of the Cauchy integral Meromorphic functions and residues The zeros of a holomorphic function Holomorphic functions as geometric mappings Harmonic functions Infinite series and products Applications of infinite sums and products Analytic continuation Topology Rational approximation theory Special classes of holomorphic functions Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings Special functions The prime number theorem Appendix A: Real analysis Appendix B: The statement and proof of Goursat's theorem References Index.
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QA331.7 .G75 2006  Unknown 
 Krantz, Steven G. (Steven George), 1951
 Boston : Birkhäuser, c2006.
 Description
 Book — xiii, 314 p. : ill. ; 24 cm.
 Summary

 * Preface Part I: Classical Function Theory * Invariant Geometry * Variations on the Theme of the Schwarz Lemma * Normal Families * The Riemann Mapping Theorem and its Generalizations * Boundary Regularity of Conformal Maps * The Boundary Behavior of Holomorphic Functions Part II: Real and Harmonic Analysis * The CauchyRiemann Equations * The Green's Function and the Poisson Kernel * Harmonic Measure * Conjugate Functions and the Hilbert Transform * Wolff's Proof of the Corona Theorem Part III: Algebraic Topics * Automorphism Groups of Domains in the Plane * Cousin Problems, Cohomology, and Sheaves * Bibliography * Index.
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QA331.7 .K733 2006  Available 