An Introduction to Sato's Hyperfunctions

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American Mathematical Soc., Jan 1, 1993 - Mathematics - 273 pages
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This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.
 

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Contents

Fundamental Properties of Holomorphic Functions
1
2 Holomorphic functions
3
3 Power series and Reinhardt domains
6
4 Linear topological spaces of holomorphic functions
8
5 Germs of holomorphic functions
11
K Runge open sets
13
7 The FourierBorel transformation
14
8 Entire functions of exponential type
16
3 Various operations
47
4 Jfunction and Kfunction
49
5 Power functions
53
6 Singular spectrum
55
7 Relation with local analytic functionals
58
8 Ordinary differential equations
61
9 Distributions and hyperfunctions
64
Cohomology Groups with Coefficients in a Sheaf
69

Analytic Functional of One Variable
23
1 The CauchyHilbert transformation
24
2 The Runge theorems
30
3 The MittagLeffler theorem
32
4 A representation of analytic functional
35
The FourierLaplace transform of an entire function of exponential type
36
K Convolution
38
Hyperfunctions of One Variable
41
Definition of hyperfunctions
43
2 Locality of hyperfunctions
45
Cohomology Groups with Coefficients in f109
109
Analytic Functionals of Several Variables
129
Hyperfunctions of Several Variables
155
Microfunctions
177
Development of Hyperfunction Theory
211
Appendix A Linear Topological Spaces
239
Appendix B Rudiments of Homological Algebra
257
Bibliography
265
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Page 1 - The main purpose of this chapter is to familiarize the reader with the notation, the definitions, and the theorems which will be used . frequently throughout this book.

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