Linear differential equations in the complex domain: problems of analytic continuation
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Mathemat. Soc.
1990
|
| Series: | Translations of mathematical monographs
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Japan. übers. |
| Physical Description: | XIV, 267 S. graph. Darst. |
| ISBN: | 0821845357 |
Staff View
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| 240 | 1 | 0 | |a Fukuso ryōiki ni okeru senkei jōbibun hōteishiki |
| 245 | 1 | 0 | |a Linear differential equations in the complex domain |b problems of analytic continuation |c Yasutaka Sibuya |
| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 1990 | |
| 300 | |a XIV, 267 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 82 | |
| 500 | |a Aus d. Japan. übers. | ||
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| 650 | 4 | |a Fonctions de plusieurs variables complexes | |
| 650 | 7 | |a Fonctions de plusieurs variables complexes |2 ram | |
| 650 | 4 | |a Prolongement analytique | |
| 650 | 7 | |a Prolongement analytique |2 ram | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Analytic continuation | |
| 650 | 4 | |a Differential equations | |
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Record in the Search Index
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| adam_text | Table of Contents
Translator s Preface xi
Preface to the Japanese Edition xiii
Chapter I. Structures of Analytic Continuation 1
§1.0. Preliminaries 1
§1.1. Holomorphic functions 1
§1.2. Power series 2
§1.3. Taylor series 4
§1.4. Structures of analytic continuation 4
§1.5. Connection matrices along a curve 8
§1.6. Structures of monodromy 12
§1.7. One to one correspondence between structures of analytic
continuation and structures of monodromy 16
§1.8. Differential equations in the ring of power series 22
§1.9. A system of fundamental solutions of a linear ordinary
differential equation 24
§1.10. Structures of analytic continuation denned by linear
differential equations 27
§1.11. Two linear ordinary differential equations which define the
same structure of analytic continuation 28
Chapter II. Existence Theorem of Grauert 31
§2.0. Preliminaries 31
§2.1. Linear groups 32
§2.2. A decomposition theorem of Cartan 35
§2.3. Proof of the Cartan theorem 37
: §2.4. A lemma of Grauert 39
§2.5. A deformation theorem of Grauert 44
§2.6. A lemma of Grauert (continued) 47
§2.7. A deformation theorem of Grauert (continued) 51
vii
i
viii TABLE OF CONTENTS
§2.8. An existence theorem 56
§2.9. An existence theorem (continued) 60
§2.10. The case of one independent variable (Theorem 2.0.1) 63
§2.11. Improvements and applications of Theorem 1.11.3. 66
Chapter III. A Theorem of G. D. Birkhoff 69
§3.0. Preliminaries 69
§3.1. Standard forms of linear ordinary differential equations at
singular points 69
§3.2. The case when coefficients are restricted to a set smaller
than @{2S) 72
§3.3. A theorem of G. D. Birkhoff 73
§3.4. A lemma of G. D. Birkhoff 75
§3.5. Proof of Lemma 3.4.3 77
§3.6. Proof of Lemma 3.4.2 79
§3.7. Proof of lemma 3.4.1 and a lemma of T. Kimura 81
§3.8. Proof of the Birkhoff theorem 84
§3.9. The case when coefficients admit a simple pole (a theorem
of M. Hukuhara) 85
§3.10. A theorem of H. L. Turrittin 91
Chapter IV. The Riemann Problem 95
§4.0. Preliminaries 95
§4.1. Transformation of a linear ordinary differential equation at
a regular singular point 96
§4.2. Normally regular singular points 98
§4.3. Linear ordinary differential equations of Fuchsian type 100
§4.4. An existence theorem over the complex plane 104
§4.5. An existence theorem of T. Kimura over the Riemann
sphere 107
§4.6. Triangulation of a differential equation of Fuchsian type 110
Chapter V. Linear Differential Equations on a Sectorial Domain 115
§5.0. Preliminaries 115
§5.1. Asymptotic expansions 115
§5.2. Linear differential equations on a sectorial domain 117
§5.3. The order of solutions at z = oo 118
§5.4. Improvement of estimates of order of solutions 120
§5.5. The case when Ao is not a nilpotent matrix 121
§5.6. The case of a single equation of higher order 124
§5.7. Existence of a cyclic vector 126
TABLE OF CONTENTS ix
§5.8. Singularity of a transformation 130
§5.9. Characterization of singular points 134
§5.10. Necessary and sufficient conditions 139
Chapter VI. The Stokes Phenomena 143
§6.0. Preliminaries 143
§6.1. Systems of fundamental solutions in the neighborhood of
z = oo 143
§6.2. The Stokes phenomena 146
§6.3. Differential equations denning the same Stokes
phenomenon 148
§6.4. Differential equations denning a given Stokes phenomenon 150
§6.5. An improvement of the decomposition theorem of Cartan 152
§6.6. An improvement of the decomposition theorem of Cartan
(continued) 159
§6.7. Proof of Theorem 6.4.1 160
§6.8. Formal and asymptotic structures 162
§6.9. Asymptotic systems at z = oo 166
§6.10. The Stokes structures 169
§6.11. Classification by means of the Stokes structures 173
Appendix 1. The Hukuhara Turrittin Theorem in Terms of
y ZV Modules 177
§A.1.0. Preliminaries 177
§ A. 1.1. Dw modules 178
§A. 1.2. Fuchsian modules 180
§A. 1.3. The general case 181
§A. 1.4. Cyclic vectors and Newton polygons 182
§ A. 1.5. Theorem A. 1.3.1 and Newton polygons 185
Appendix 2. Gevrey Asymptotics 189
§A.2.0. Preliminaries 189
§A.2.1. Properties of C[[z ]], 192
§A.2.2. Properties of s/s(R0,a,b) 196
§A.2.3. Gevrey asymptotic solutions 201
§A.2.4. Applications of Lemma A.2.0.5 207
§A.2.5. Phragmen Lindelof theorem in a cohomological form 211
x TABLE OF CONTENTS
Appendix 3. Cohomological Methods 215
§A.3.0. Preliminaries 215
§A.3.1. Irregularity 216
§A.3.2. Classification by means of cohomologies 220
§A.3.3. Analytization 224
§A.3.4. Injectivity of Z) modules sfsja{d) 225
Appendix 4. /c Summability 229
§A.4.0. Preliminaries 229
§A.4.1. /c summability of formal solutions 232
§A.4.2. The Turrittin problem 235
Appendix 5. Differential Equations Containing Parameters 241
§A.5.0. Preliminaries 241
§A.5.1. The Majima asymptotics 241
§A.5.2. Isomonodromic deformations 246
§A.5.3. Isoformal deformations 253
§A.5.4. Singular perturbations and the Gevrey asymptotics 254
References 257
Index 265
|
| any_adam_object | 1 |
| author | Shibuya, Yasutaka 1930- |
| author_GND | (DE-588)121295656 |
| author_facet | Shibuya, Yasutaka 1930- |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.354 |
| dewey-search | 515/.354 |
| dewey-sort | 3515 3354 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:10:55Z |
| institution | BVB |
| isbn | 0821845357 |
| language | English Japanese |
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| physical | XIV, 267 S. graph. Darst. |
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| spelling | Shibuya, Yasutaka 1930- Verfasser (DE-588)121295656 aut Fukuso ryōiki ni okeru senkei jōbibun hōteishiki Linear differential equations in the complex domain problems of analytic continuation Yasutaka Sibuya Providence, RI American Mathemat. Soc. 1990 XIV, 267 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 82 Aus d. Japan. übers. Equations différentielles ram Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Prolongement analytique Prolongement analytique ram Équations différentielles Analytic continuation Differential equations Functions of several complex variables Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Analytische Fortsetzung (DE-588)4142347-1 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 s Analytische Fortsetzung (DE-588)4142347-1 s DE-604 Differentialgleichung (DE-588)4012249-9 s Mehrere komplexe Variable (DE-588)4169285-8 s Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s DE-188 Translations of mathematical monographs 82 (DE-604)BV000002394 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002664778&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shibuya, Yasutaka 1930- Linear differential equations in the complex domain problems of analytic continuation Translations of mathematical monographs Equations différentielles ram Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Prolongement analytique Prolongement analytique ram Équations différentielles Analytic continuation Differential equations Functions of several complex variables Differentialgleichung (DE-588)4012249-9 gnd Analytische Fortsetzung (DE-588)4142347-1 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4142347-1 (DE-588)4206889-7 (DE-588)4169285-8 (DE-588)4353441-7 |
| title | Linear differential equations in the complex domain problems of analytic continuation |
| title_alt | Fukuso ryōiki ni okeru senkei jōbibun hōteishiki |
| title_auth | Linear differential equations in the complex domain problems of analytic continuation |
| title_exact_search | Linear differential equations in the complex domain problems of analytic continuation |
| title_full | Linear differential equations in the complex domain problems of analytic continuation Yasutaka Sibuya |
| title_fullStr | Linear differential equations in the complex domain problems of analytic continuation Yasutaka Sibuya |
| title_full_unstemmed | Linear differential equations in the complex domain problems of analytic continuation Yasutaka Sibuya |
| title_short | Linear differential equations in the complex domain |
| title_sort | linear differential equations in the complex domain problems of analytic continuation |
| title_sub | problems of analytic continuation |
| topic | Equations différentielles ram Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Prolongement analytique Prolongement analytique ram Équations différentielles Analytic continuation Differential equations Functions of several complex variables Differentialgleichung (DE-588)4012249-9 gnd Analytische Fortsetzung (DE-588)4142347-1 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| topic_facet | Equations différentielles Fonctions de plusieurs variables complexes Prolongement analytique Équations différentielles Analytic continuation Differential equations Functions of several complex variables Differentialgleichung Analytische Fortsetzung Lineare Differentialgleichung Mehrere komplexe Variable Lineare gewöhnliche Differentialgleichung |
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