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.
Author(s): O.P. Misra and J.L. Lavoine (Eds.)
Series: North-Holland Mathematics Studies 119
Publisher: Elsevier Science Ltd
Year: 1986
Language: English
Pages: ii-vi, 1-332
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
