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

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