Elementary Introduction to New Generalized Functions

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Page iii

Copyright page
Page iv

Dedication
Page v

Foreword
Pages vii-x

Part I An Elementary Approach to the New Generalized Functions
Pages 1-5

Chapter 1 Generalized Functions
Pages 7-34

Chapter 2 Generalized Analysis
Pages 35-67

Chapter 3 Some Linear Cauchy Problems
Pages 69-93

Part II Tempered Generalized Functions
Pages 95-96

Chapter 4 The Fourier Transform and the Tempered Generalized Functions
Pages 97-126

Chapter 5 The Convolution Product
Pages 127-148

Chapter 6 Computations on Tempered Generalized Functions
Pages 149-177

Part III New Solutions of Partial Differential Equations
Pages 179-183

Chapter 7 Linear Equations
Pages 185-206

Chapter 8 Nonlinear Equations
Pages 207-240

Appendix I The Removal of Divergences in Perturbation Theory
Pages 241-243

Appendix 2 Generalized Functions on Closed Sets and Whitney's Extension Theorem
Pages 244-245

Appendix 3 Generalized Functions and Waelbroeck's Theory of Analysis in Quotient Spaces
Pages 246-247

Appendix 4 Generalized Functions on Hilbert Spaces
Pages 248-254

Appendix 5 Complements to N.G.F.: Analytic Continuation and Composition of Generalized Functions
Pages 255-259

Appendix 6 General Existence Results for Linear Partial Differential Equations With C∞ Coefficients
Pages 260-261

Appendix 7 Introduction to Distributions and Their Multiplication for first Year University Students
Pages 262-269

Bibliographic Notes
Pages 271-273

Index
Pages 274-277

References
Pages 278-281