Transform Analysis of Generalized Functions

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Elsevier, Jan 1, 1986 - Mathematics - 331 pages
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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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Contents

CHAPTER 0 PRELIMINARIES
1
CHAPTER 1 FINITE PARTS OF INTEGRALS
7
CHAPTER 2 BASE SPACES
19
CHAPTER 3 DEFINITION OF DISTRIBUTIONS
25
CHAPTER 4 PROPERTIES OF GENERALIZED FUNCTIONS AND DISTRIBUTIONS
35
CHAPTER 5 OPERATIONS ON GENERALIZED FUNCTIONS AND DISTRIBUTIONS
47
CHAPTER 6 OTHER OPERATIONS ON DISTRIBUTIONS
77
CHAPTER 7 THE FOURIER TRANSFORMATION
91
CHAPTER 9 APPLICATIONS OF THE LAPLACE TRANSFORMATION
145
CHAPTER 10 THE STIELTJES TRANSFORMATION
207
CHAPTER 11 THE MELLIN TRANSFORMATION
227
CHAPTER 12 HANKEL TRANSFORMATION AND BESSEL SERIES
269
BIBLIOGRAPHY
315
INDEX OF SYMBOLS
329
AUTHOR INDEX
331
Copyright

CHAPTER 8 THE LAPLACE TRANSFORMATION
107

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