Introduction to hyperfunctions
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Tokyo
KTK Scientif. Publ. u.a.
1988
|
| Schriftenreihe: | Mathematics and its applications / Japanese series
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 001 | BV002756832 | ||
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| 005 | 20190301 | ||
| 007 | t| | ||
| 008 | 900719s1988 xx d||| |||| 00||| eng d | ||
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| 035 | |a (DE-599)BVBBV002756832 | ||
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| 041 | 0 | |a eng | |
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| 084 | |a MAT 465f |2 stub | ||
| 100 | 1 | |a Kaneko, Akira |d 1961- |e Verfasser |0 (DE-588)124213138 |4 aut | |
| 240 | 1 | 0 | |a Chōkansū-nyūmon |
| 245 | 1 | 0 | |a Introduction to hyperfunctions |c by A. Kaneko |
| 264 | 1 | |a Tokyo |b KTK Scientif. Publ. u.a. |c 1988 | |
| 300 | |a XIII, 458 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Japanese series |v 3 | |
| 500 | |a Aus d. Japan. übers. | ||
| 650 | 0 | 7 | |a Hyperfunktion |0 (DE-588)4161056-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperfunktion |0 (DE-588)4161056-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 810 | 2 | |a Japanese series |t Mathematics and its applications |v 3 |w (DE-604)BV000613779 |9 3 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-001762301 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 465f 2001 A 20144 |
|---|---|
| DE-BY-TUM_katkey | 483616 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010423486 |
| _version_ | 1820869046739927040 |
| adam_text | CONTENTS
SERIES EDITOR S PREFACE v
PREFACE vii
INTRODUCTION 1
PART I
PREFACE TO PART I 9
CHAPTER 1. HYPERFUNCTIONS OF A SINGLE
VARIABLE 11
§ 1. Definitions and Elementary Operations 11
§2. Localizability 16
§3. Embedding Functions into the Space of
Hyperfunctions 19
§4. Flabby Sheaves 34
§5. Proofs of Fundamental Theorems* 37
§6. Singular Spectrum 41
§7. Microfunctions* 47
§8. Local and Micro Local Operators 55
CHAPTER 2. HOLOMORPHIC FUNCTIONS OF SEVERAL
VARIABLES 65
§1. Elementary Properties 65
§2. Analytic Continuation 74
§3. Radon Decomposition of Holomorphic
Functions* 83
CHAPTER 3. HYPERFUNCTIONS OF SEVERAL
VARIABLES 95
§1. Intuitive Definition 95
§2. Operations on Hyperfunctions I 102
xii Contents
§3. Proofs of Fundamental Facts* 112
§4. Operations on Hyperfunctions II 119
§5. Embedding Ordinary Functions* 135
CHAPTER 4. VARIOUS STRUCTURES OF
HYPERFUNCTIONS* 151
§1. Topology 151
§2. Hyperfunctions on Manifolds 166
§3. Hyperfunctions with Holomorphic
Parameters 176
§4. Hyperfunctions with Support Contained in a
Half Space 190
§5. Hyperfunctions with Support Contained in a
Hypersurface 201
§6. Microfunctions 210
PART II
PREFACE TO PART II 235
CHAPTER 5. SHEAF COHOMOLOGY* 237
§1. Flabby Sheaves 237
§2. Preparation from Homological Algebra .... 246
§3. Cohomologies via Flabby Resolutions 251
§4. Dimensions of Sheaves and Codimensions of
Sets 259
§5. Cech Cohomology 263
§6. Higher Direct Images 276
§7. Soft Sheaves 281
CHAPTER 6. COHOMOLOGICAL PROPERTIES OF
HOLOMORPHIC FUNCTIONS* 287
§1. The Cousin Problem in Cylindrical Domains
287
§2. Domain of Holomorphy 294
§3. Runge Domains and Cohomology Vanishing
Theorem 301
§4. Grauert s Theorem 310
§5. Pure Codimensionality of R in C 317
Contents xiii
CHAPTER 7. COHOMOLOGICAL PROPERTIES OF
HYPERFUNCTIONS* 329
§ 1. Cohomological Definition of Hyperfunctions
329
§2. Embedding of Real Analytic Functions 341
§3. Flabbiness of the Sheaf of Hyperfunctions . . . 350
§4. Cohomological Definition of Hyperfunctions with
Holomorphic Parameters 357
CHAPTER 8. FOURIER TRANSFORMS 367
§ 1. Fourier Transforms of Hyperfunctions with
Compact Support 368
§2. Fourier Transforms of Exponentially Decreasing
Hyperfunctions 375
§3. Fourier Transforms of Slowly Increasing
Hyperfunctions 383
§4. Relationships among Various Spaces of
Hyperfunctions* 389
§5. Localizability* 400
§6. Topology and Duality* 407
SOLUTIONS TO EXERCISES 419
POSTFACE 441
BIBLIOGRAPHY 445
INDEX 453
GLOSSARY OF NOTATION 457
|
| any_adam_object | 1 |
| author | Kaneko, Akira 1961- |
| author_GND | (DE-588)124213138 |
| author_facet | Kaneko, Akira 1961- |
| author_role | aut |
| author_sort | Kaneko, Akira 1961- |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV002756832 |
| classification_rvk | SK 780 |
| classification_tum | MAT 465f |
| ctrlnum | (OCoLC)243428681 (DE-599)BVBBV002756832 |
| dewey-full | 515.782 515.7'82 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.782 515.7'82 |
| dewey-search | 515.782 515.7'82 |
| dewey-sort | 3515.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002756832 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T10:47:24Z |
| institution | BVB |
| isbn | 9027728372 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001762301 |
| oclc_num | 243428681 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-739 DE-703 DE-706 DE-188 DE-11 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-703 DE-706 DE-188 DE-11 |
| physical | XIII, 458 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | KTK Scientif. Publ. u.a. |
| record_format | marc |
| series2 | Mathematics and its applications / Japanese series |
| spellingShingle | Kaneko, Akira 1961- Introduction to hyperfunctions Hyperfunktion (DE-588)4161056-8 gnd |
| subject_GND | (DE-588)4161056-8 |
| title | Introduction to hyperfunctions |
| title_alt | Chōkansū-nyūmon |
| title_auth | Introduction to hyperfunctions |
| title_exact_search | Introduction to hyperfunctions |
| title_full | Introduction to hyperfunctions by A. Kaneko |
| title_fullStr | Introduction to hyperfunctions by A. Kaneko |
| title_full_unstemmed | Introduction to hyperfunctions by A. Kaneko |
| title_short | Introduction to hyperfunctions |
| title_sort | introduction to hyperfunctions |
| topic | Hyperfunktion (DE-588)4161056-8 gnd |
| topic_facet | Hyperfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001762301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000613779 |
| work_keys_str_mv | AT kanekoakira chokansunyumon AT kanekoakira introductiontohyperfunctions |