Transform Analysis of Generalized Functions ( Volume 119 )

Publication series :Volume 119

Author: Misra   O. P.;Lavoine   J. L.  

Publisher: Elsevier Science‎

Publication year: 1986

E-ISBN: 9780080872308

P-ISBN(Paperback): 9780444878854

P-ISBN(Hardback):  9780444878854

Subject: O172 Calculus;O177 functional analysis

Language: ENG

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Description

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.

Chapter

Front Cover

pp.:  1 – 4

Copyright Page

pp.:  5 – 8

Table of Contents

pp.:  8 – 16

CHAPTER 0. PRELIMINARIES

pp.:  16 – 22

CHAPTER 1. FINITE PARTS OF INTEGRALS

pp.:  22 – 34

CHAPTER 2. BASE SPACES

pp.:  34 – 40

CHAPTER 3. DEFINITION OF DISTRIBUTIONS

pp.:  40 – 50

CHAPTER 4. PROPERTIES OF GENERALIZED FUNCTIONS AND DISTRIBUTIONS

pp.:  50 – 62

CHAPTER 5. OPERATIONS ON GENERALIZED FUNCTIONS AND DISTRIBUTIONS

pp.:  62 – 92

CHAPTER 6. OTHER OPERATIONS ON DISTRIBUTIONS

pp.:  92 – 106

CHAPTER 7. THE FOURIER TRANSFORMATION

pp.:  106 – 122

CHAPTER 8. THE LAPLACE TRANSFORMATION

pp.:  122 – 160

CHAPTER 9. APPLICATIONS OF THE LAPLACE TRANSFORMATION

pp.:  160 – 222

CHAPTER 10. THE STIELTJES TRANSFORMATION

pp.:  222 – 242

CHAPTER 11. THE MELLIN TRANSFORMATION

pp.:  242 – 284

CHAPTER 12. HANKEL TRANSFORMATION AND BESSEL SERIES

pp.:  284 – 330

BIBLIOGRAPHY

pp.:  330 – 344

INDEX OF SYMBOLS

pp.:  344 – 346

AUTHOR INDEX

pp.:  346 – 348

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