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Functional analysis : fundamentals and applications / Michel Willem.

By: Material type: TextLanguage: English Series: Cornerstones (Birkhäuser Verlag)Publication details: Cham : Springer International Publishing AG, 2023.Edition: Second editionDescription: 259 p. : illustrations (black and white)ISBN:
  • 9783031091490
Subject(s): Additional physical formats: Print version:: Functional analysis.DDC classification:
  • 515.7 23/eng/20230201 WIL
Online resources:
Contents:
Intro Preface to the Second Edition Preface to the First Edition Acknowledgments Contents 1 Distance 1.1 Real Numbers 1.2 Metric Spaces 1.3 Continuity 1.4 Convergence 1.5 Comments 1.6 Exercises for Chap.1 2 The Integral 2.1 The Cauchy Integral 2.2 The Lebesgue Integral 2.3 Multiple Integrals 2.4 Change of Variables 2.5 Comments 2.6 Exercises for Chap.2 3 Norms 3.1 Banach Spaces 3.2 Continuous Linear Mappings 3.3 Hilbert Spaces 3.4 Spectral Theory 3.5 Comments 3.6 Exercises for Chap.3 4 Lebesgue Spaces 4.1 Convexity 4.2 Lebesgue Spaces 4.3 Regularization 4.4 Compactness 4.5 Comments 4.6 Exercises for Chap.4 5 Duality 5.1 Weak Convergence 5.2 James Representation Theorem 5.3 Duality of Hilbert Spaces 5.4 Duality of Lebesgue Spaces 5.5 Comments 5.6 Exercises for Chap.5 6 Sobolev Spaces 6.1 Weak Derivatives 6.2 Cylindrical Domains 6.3 Smooth Domains 6.4 Embeddings 6.5 Comments 6.6 Exercises for Chap.6 7 Capacity 7.1 Capacity 7.2 Variational Capacity 7.3 Functions of Bounded Variations 7.4 Perimeter 7.5 Distribution Theory 7.6 Comments 7.7 Exercises for Chap.7 8 Elliptic Problems 8.1 The Laplacian 8.2 Eigenfunctions 8.3 Symmetrization 8.4 Elementary Solutions 8.5 Comments 8.6 Exercises for Chap.8 9 Appendix: Topics in Calculus 9.1 Change of Variables 9.2 Surface Integrals 9.3 The Morse-Sard Theorem 9.4 The Divergence Theorem 9.5 Comments 10 Epilogue: Historical Notes on Functional Analysis 10.1 Integral Calculus 10.2 Measure and Integral 10.3 Differential Calculus 10.4 Comments References Index of Notation Index
Summary: This textbook presents the principles of functional analysis in a clear and concise way. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
General Books CUTN Central Library Sciences Non-fiction 515.7 WIL (Browse shelf(Opens below)) Available 54649
General Books CUTN Central Library Sciences Non-fiction 515.7 WIL (Browse shelf(Opens below)) Available 54650

Previous edition: New York: Birkhäuser, 2013.

Includes bibliographical references and indexes.


Intro
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
1 Distance
1.1 Real Numbers
1.2 Metric Spaces
1.3 Continuity
1.4 Convergence
1.5 Comments
1.6 Exercises for Chap.1
2 The Integral
2.1 The Cauchy Integral
2.2 The Lebesgue Integral
2.3 Multiple Integrals
2.4 Change of Variables
2.5 Comments
2.6 Exercises for Chap.2
3 Norms
3.1 Banach Spaces
3.2 Continuous Linear Mappings
3.3 Hilbert Spaces
3.4 Spectral Theory
3.5 Comments
3.6 Exercises for Chap.3
4 Lebesgue Spaces 4.1 Convexity
4.2 Lebesgue Spaces
4.3 Regularization
4.4 Compactness
4.5 Comments
4.6 Exercises for Chap.4
5 Duality
5.1 Weak Convergence
5.2 James Representation Theorem
5.3 Duality of Hilbert Spaces
5.4 Duality of Lebesgue Spaces
5.5 Comments
5.6 Exercises for Chap.5
6 Sobolev Spaces
6.1 Weak Derivatives
6.2 Cylindrical Domains
6.3 Smooth Domains
6.4 Embeddings
6.5 Comments
6.6 Exercises for Chap.6
7 Capacity
7.1 Capacity
7.2 Variational Capacity
7.3 Functions of Bounded Variations
7.4 Perimeter
7.5 Distribution Theory 7.6 Comments
7.7 Exercises for Chap.7
8 Elliptic Problems
8.1 The Laplacian
8.2 Eigenfunctions
8.3 Symmetrization
8.4 Elementary Solutions
8.5 Comments
8.6 Exercises for Chap.8
9 Appendix: Topics in Calculus
9.1 Change of Variables
9.2 Surface Integrals
9.3 The Morse-Sard Theorem
9.4 The Divergence Theorem
9.5 Comments
10 Epilogue: Historical Notes on Functional Analysis
10.1 Integral Calculus
10.2 Measure and Integral
10.3 Differential Calculus
10.4 Comments
References
Index of Notation
Index

This textbook presents the principles of functional analysis in a clear and concise way. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces.

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