An introduction to Sato's hyperfunctions: = Satō-chokansū-nyūmon
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
Amer. Math. Soc.
1993
|
| Series: | Translations of mathematical monographs
129 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Japan. übers. |
| Physical Description: | XII, 273 S. graph. Darst. |
| ISBN: | 0821845713 |
Staff View
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| 100 | 1 | |a Morimoto, Mitsuo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to Sato's hyperfunctions |b = Satō-chokansū-nyūmon |c Mitsuo Morimoto |
| 246 | 1 | 1 | |a Satō-chokansū-nyūmon |
| 264 | 1 | |a Providence, RI |b Amer. Math. Soc. |c 1993 | |
| 300 | |a XII, 273 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804123237194399744 |
|---|---|
| adam_text | Contents
Preface to the English Edition ix
Preface to the Japanese Edition xi
Chapter 1. Fundamental Properties of Holomorphic Functions 1
Summary 1
§1. Continuous functions, measures, and distributions 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
§6. Runge open sets 13
§7. The Fourier Borel transformation 14
§8. Entire functions of exponential type 16
Chapter 2. Analytic Functional of One Variable 23
Summary 23
§1. The Cauchy Hilbert transformation 24
§2. The Runge theorems 30
§3. The Mittag Leffler theorem 32
§4. A representation of analytic functionals 35
§ 5. The Fourier Laplace transform of an entire function of
exponential type 36
§6. Convolution 38
Chapter 3. Hyperfunctions of One Variable 41
Summary 41
§ 1. Definition of hyperfunctions 42
§2. Locality of hyperfunctions 45
§3. Various operations 47
§4. J function and T function 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
V
vi CONTENTS
Chapter 4. Cohomology Groups with Coefficients in a Sheaf 69
Summary 69
§1. Sheaf 69
§2. Presheaf 74
§3. Cohomology groups with coefficients in a sheaf 79
§4. Relative cohomology groups 85
§5. The cohomology group of a covering 87
§6. The theory of sheaves over paracompact spaces 93
§7. The derived sheaf of relative cohomology groups 97
§8. Pure codimensionality and the flabby dimension of a sheaf 99
§9. Theorems on pure codimensionality 104
Chapter 5. Cohomology Groups with Coefficients in 9 109
Summary 109
§1. Domain of holomorphy (review) 109
§2. A method of calculation of relative cohomology groups with
coefficients in 115
§3. Vanishing of relative cohomology groups 119
Chapter 6. Analytic Functionals of Several Variables 129
Summary 129
§1. Integral representation of holomorphic functions 129
§2. Linearly convex compact sets 133
§3. Dual space of {K) 134
§4. The Laplace Martineau transform of entire functions of
exponential type 141
§5. The Martineau Harvey duality theorem 146
Chapter 7. Hyperfunctions of Several Variables 155
Summary 155
§ 1. Definition of hyperfunctions and their fundamental properties 155
§2. Hyperfunctions as a class of holomorphic functions 158
§3. Hyperfunctions with compact support 163
§4. The boundary value of a holomorphic function 165
§5. Injectivity of the boundary value operator br 170
Chapter 8. Microfunctions 177
Summary 177
§1. The decomposition of singularities of hyperfunctions of one
variable 178
§2. Conormal sphere bundle 181
§3. Vanishing of the relative cohomology group 183
§4. The Mayer Vietoris theorem 188
§5. Definition of microfunction 190
§6. Relation of hyperfunctions and microfunctions 197
§7. Microfunctions and the analyticity of hyperfunctions 204
CONTENTS vii
Chapter 9. Development of Hyperfunction Theory 211
Summary 211
§1. Hyperfunctions on a real analytic manifold 211
§2. Edge of the Wedge theorem 214
§3. Micro analyticity of hyperfunctions 218
§4. Operations on hyperfunctions 222
§5. Sato s fundamental theorem 228
§6. Lorentz invariant hyperfunctions 232
Appendix A. Linear Topological Spaces 239
Summary 239
§1. Linear topological spaces 239
§2. Limit of linear spaces 243
§3. Limit of linear topological spaces 244
§4. FS spaces 246
§5. DFS spaces 249
§6. Duality of FS spaces and DFS spaces 253
Appendix B. Rudiments of Homological Algebra 257
Summary 257
§1. Exact sequences 257
§2. Cohomology group of a complex 258
Appendix C. Bibliographical Notes 261
Measure theory and function theory 261
Distribution theory and functional analysis 261
Early papers on hyperfunctions 262
Sheaf theory and homological algebra 262
Analytic functional 263
Microfunctions 263
Theoretical physics and the Edge of the Wedge theorem 263
More recent literature 264
Bibliography 265
Subject Index 269
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| indexdate | 2024-07-09T17:26:34Z |
| institution | BVB |
| isbn | 0821845713 |
| language | English |
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| physical | XII, 273 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Amer. Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Morimoto, Mitsuo Verfasser aut An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon Mitsuo Morimoto Satō-chokansū-nyūmon Providence, RI Amer. Math. Soc. 1993 XII, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 129 Aus dem Japan. übers. Hyperfunktion (DE-588)4161056-8 gnd rswk-swf Hyperfunktion (DE-588)4161056-8 s DE-604 Translations of mathematical monographs 129 (DE-604)BV000002394 129 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005874647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morimoto, Mitsuo An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon Translations of mathematical monographs Hyperfunktion (DE-588)4161056-8 gnd |
| subject_GND | (DE-588)4161056-8 |
| title | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon |
| title_alt | Satō-chokansū-nyūmon |
| title_auth | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon |
| title_exact_search | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon |
| title_full | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon Mitsuo Morimoto |
| title_fullStr | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon Mitsuo Morimoto |
| title_full_unstemmed | An introduction to Sato's hyperfunctions = Satō-chokansū-nyūmon Mitsuo Morimoto |
| title_short | An introduction to Sato's hyperfunctions |
| title_sort | an introduction to sato s hyperfunctions sato chokansu nyumon |
| title_sub | = Satō-chokansū-nyūmon |
| topic | Hyperfunktion (DE-588)4161056-8 gnd |
| topic_facet | Hyperfunktion |
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