Elementary introduction to new gegeralized functions

Title page
Foreword
PART 1: AN ELEMENTARY APPROACH TO THE NEW GENERALIZED FUNCTIONS
Chapter 1 Generalized Functions
1.1 Definition of the genera1ized functions on R^n
1.2 Generalized functions on an open set Ω of R^n
1.3 Local properties of generalized functions
1.4 Nonlinear properties of generalized functions
1.5 Distributions: definitions and examples
Chapter 2 Generalized Analysis
2.1 Genera1ized numbers and pointva1ues of generalized functions
2.2 The integration on compact sets of generalized functions
2.3 Primitives
2.4 Application to distributions
2.5 Generalized distributions
Chapter 3 Some Linear Cauchy Problems
3.1 Introduction
3.2 Existence and Uniqueness Results
3.3 Approximate and Asymptotic expansions of generalized functions
3.4 The equation X' = ig AX in the non communicative case
3.5 The equation X' = ig AX when A has no compact support
PART II TEMPERED GENERALIZED FUNCTIONS
Chapter 4 The Fourier Transform and the Tempered Generalized Functions
4.1 The tempered generalized functions
4.2 Integration of the tempered generalized functions
4.3 The Fourier transform of the tempered generalized functions
4.4 The tempered distributions
Chapter 5 The Convolution Product
5.1 Convo1ution of genera1ized functions
5.2 Convo1ution of distributions
5.3 Convo1ution of tempered genera1ized functions
Chapter 6 Computations on Tempered Generalized Functions
6.1 Introduction
6.2 The vector va1ued tempered generalized functions
6.3 The free field
6.4 Computations
PART III NEW SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Chapter 7 Linear Equations
7.1 The ? equation
7.2 A Cauchy prob1em for linear wave equations
7.3 A linear Cauchy-Kova1evska theorem
Chapter 8 Nonlinear Equations
8.1 An existence result for wave equations including a nonlinear term with a boundedness property
8.2 Uniqueness and regu1arity results
8.3 An existence result for wave equations with unbounded second members
8.4 A regu1arity result
Appendix 1 The Removal of Divergences in Perturbation Theory
Appendix 2 Generalized Functions on Closed Sets and Whitney's Extension Theorem
Appendix 3 Generalized Functions and Waelbroeck's Analysis in Quotient Spaces
Appendix 4 Generalized Functions on Hilbert Spaces
Appendix 5 Complements to N.G.F.: Analytic Continuation and Composition of Generalized Functions
Appendix 6 General Existence Results for Linear Partial Differentiai Equations with C^∞ Coefficients
Appendix 7 Introduction to Distributions and their Multiplication for First Year University Students
Bibliographic Notes
Index
References