Book:Nino Boccara/Functional Analysis: An Introduction for Physicists

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Nino Boccara: Functional Analysis: An Introduction for Physicists

Published $1990$, Academic Press

ISBN 978-0121088101.


Subject Matter

Functional Analysis

Contents

Foreword

Notations

Chapter 1. Measure and Integration
1. Measurable Functions
2. Positive Measures
3. Integral of Measurable Functions
4. Lebesgue's Dominated Convergence Theorem
5. Fubini's Theorem
Appendix
Notes
Problems
Solutions
Chapter 2. Lebesgue Spaces
1. Convex Functions and Inequalities
2. ${\cal L}^p$ and $L^p$ Spaces
3. Dense Subspaces in $L^p$
4. Fourier Transform
5. Laplace Transform
Note
Problems
Solutions
Chapter 3. Hilbert Spaces
1. Scalar Product
2. Hilbert Spaces
3. Orthogonal Systems
Appendix
Notes
Problems
Solutions
Chapter 4. Distributions
1. Test Functions and Distributions
2. Differentiation
3. Convergence in $\cal D'$
4. Convolution
5. Fourier Series
6. Fourier Transform of Tempered Distributions
7. Laplace Transform
Problems
Solutions
Chapter 5. Linear Operators
1. Preliminaries
2. Bounded Linear Operators
3. Compact Operators
4. Unbounded Linear Operators
5. Spectral Theory
Appendix
Problems
Solutions

References

Index