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

Nino Boccara: Functional Analysis: An Introduction for Physicists

Published $\text {1990}$, 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