Distributions and the Boundary Values of Analytic Functions

Fore wordPrefaceChapter I. Distributions 1. Introduction 1.1 Preliminaries 1.2 Some Spaces of Testing Functions 1.3 Schwartz Distributions 1.4 Distributions of Finite Order 1.5 Convolution and Regularization 1.6 Sobolev Spaces 1.7 Testing Functions of Rapid Decay and Distributions of Slow Growth 1.8 Fourier TransformsChapter II. The Laplace Transform 2.1 Laplace Transforms of Distributions with Arbitrary Support 2.2 Laplace Transforms of Distributions in D' 2.3 Laplace Transforms of Distribution in E'Chapter III. Distributional Boundary Values of Analytic Functions 3. Introduction 3.1 Causal Operators 3.2 Representation Theorems for Half Plane Holomorphic Functions with S' Boundary Behavior 3.3 Boundary Value Theorems and Generalized Hubert Transforms 3.4 Analytic Continuation and Uniqueness 3.5 Passive Operators 3.6 Notes and RemarksAppendix I. Representation of Positive-Real MatricesAppendix II. Supplementary RemarksBibliographyIndex