Spaces of Fundamental and Generalized Functions

Preface to the Russian EditionChapter I Linear Topological Spaces 1. Definition of a Linear Topological Space 2. Normed Spaces. Comparability and Compatibility of Norms 3. Countably Normed Spaces 4. Continuous Linear Functional and the Conjugate Space 5. Topology in a Conjugate Space 6. Perfect Spaces 7. Continuous Linear Operators 8. Union of Countably Normed Spaces Appendix 1. Elements, Functionals, Operators Depending on a Parameter Appendix 2. Differentiate Abstract Functions Appendix 3. Operators Depending on a Parameter Appendix 4. Integration of Continuous Abstract Functions with Respect to the ParameterChapter II Fundamental and Generalized Functions 1. Definition of Fundamental and Generalized Functions 2. Topology in the Spaces K{Mp} and Z{Mp} 3. Operations with Generalized Functions 4. Structure of Generalized FunctionsChapter III Fourier Transformations of Fundamental and Generalized Functions 1. Fourier Transformations of Fundamental Functions 2. Fourier Transforms of Generalized Functions 3. Convolution of Generalized Functions and Its Connection to Fourier Transforms 4. Fourier Transformation of Entire Analytic FunctionsChapter IV Spaces of Type S 1. Introduction 2. Various Modes of Defining Spaces of Type S 3. Topological Structure of Fundamental Spaces 4. Simplest Bounded Operations in Spaces of Type S 5. Differential Operators 6. Fourier Transformations 7. Entire Analytic Functions as Elements or Multipliers in Spaces of Type S 8. The Question of the Nontriviality of Spaces of Type S 9. The Case of Several Independent Variables Appendix 1. Generalization of Spaces of Type S Appendix 2. Spaces of Type WNotes and ReferencesBibliographyIndex