Front Cover; Distributions and their Applications in Physics; Copyright Page; Table of Contents; Foreword; Editor's Note; CHAPTER 1. Normed and Countably-normed Spaces; 1.1. Topological Spaces; 1.2. Metric Spaces; 1.3. Topological Linear Spaces; 1.4. Normed Spaces; 1.5. Countably-Normed Spaces; 1.6. Continuous Linear Functionals; 1.7. The Hahn-Banach Theorem; 1.8. Dual Spaces, Strong and Weak Topologies on Dual Spaces; 1.9. Strong and Weak Topologies on Initial Spaces; 1.10. The Union and Direct Sum of Countably-Normed Spaces; 1.11. Linear Operators; CHAPTER 2. Test Function Spaces.

6.2. Multiplication of Distributions by Infinitely Differentiable Functions6.3. The Multiplication of Distributions; 6.4. Differentiation of Distributions; 6.5. Some Applications; CHAPTER 7. Distributions with Compact Support and the General Structure of Tempered Distributions; 7.1. The space [epsilon]' as the Space of Distributions with Compact Support; 7.2. A System of Integral Norms on A; 7.3. Tempered Distributions as Derivatives of Slowly Increasing Functions; 7.4. The Structure of Distributions which are Concentrated at a Point; CHAPTER 8. Functions with Non-integrable Algebraic Singularities.

10.3· The Convolution Theorem10.4. Fourier Transforms of Distributions in '; 10.5. The Calculation of the Fourier Transforms of Certain Distributions by Analytic Continuation; 10.6. A Fundamental Lemma in the Theory of Fourier-Laplace Transforms of Distributions; 10.7. Fourier-Laplace Transforms of Distributions; 10.8. The Product of Distributions in a Certain Class; CHAPTER 11. Distributions Connected with the Light Cone; 11.1. Distributions which are Concentrated in a Smooth Surface; 11.2· Distributions Concentrated on a Cone; 11·3· The Solution of the Cauchy Problem for the Wave Equation.