Transform Analysis of Generalized Functions

O.P. Misra and J.L. Lavoine (Eds.)0444878858, 9780444878854, 9780080872308

Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series. Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here. The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.

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Table of contents :
Content:
Edited by
Pages ii-iii

Copyright page
Page iv

Preface
Pages v-vi
O.P. Misra, Jean Lavoine

Chapter 0 Preliminaries
Pages 1-6

Chapter 1 Finite Parts of Integrals
Pages 7-17

Chapter 2 Base Spaces
Pages 19-24

Chapter 3 Definition of Distributions
Pages 25-33

Chapter 4 Properties of Generalized Functions and Distributions
Pages 35-45

Chapter 5 Operations of Generalized Functions and Distributions
Pages 47-75

Chapter 6 Other Operations on Distributions
Pages 77-89

Chapter 7 The Fourier Transformation
Pages 91-105

Chapter 8 The Laplace Transformation
Pages 107-144

Chapter 9 Applications of the Laplace Transformation
Pages 145-205

Chapter 10 The Stieltjes Transformation
Pages 207-225

Chapter 11 The Mellin Transformation
Pages 227-268

Chapter 12 Hankel Transformation and Bessel Series
Pages 269-314

Bibliography
Pages 315-327

Index of Symbols
Page 329

Author Index
Pages 331-332