Fuchsian differential equations: with special emphasis on the Gauss-Schwarz theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Braunschweig u.a.
Vieweg
1987
|
| Series: | Aspects of mathematics / E.
11. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturaturverz. S. 204 - 214 |
| Physical Description: | XIV, 214 S. graph. Darst. |
| ISBN: | 3528089717 |
Staff View
MARC
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| 100 | 1 | |a Yoshida, Masaaki |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fuchsian differential equations |b with special emphasis on the Gauss-Schwarz theory |
| 264 | 1 | |a Braunschweig u.a. |b Vieweg |c 1987 | |
| 300 | |a XIV, 214 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Aspects of mathematics / E. |v 11. | |
| 500 | |a Literaturaturverz. S. 204 - 214 | ||
| 650 | 4 | |a Differential equations, Linear | |
| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
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| adam_text | Contents
Introduction
Notations
Part I
Chapter 1 Hypergeometric Differential Equations 1
§ 1.1 Hypergeometric Series 1
§ 1.2 Hypergeometric Equations 2
§ 1.3 Contiguity Relations 3
§ 1.4 Euler s Integral Representation 5
§ 1.5 Barnes Integral Representation 11
§ 1.6 Confluent Hypergeometric Equations 12
Chapter 2 General Theory of Differential Equations I ....14
§ 2.1 How to Write Differential Equations 14
§ 2.2 Cauchy s Fundamental Theorem 15
§ 2.3 Monodromy Representations of Differential
Equations 16
§ 2.4 Regular Singularities 18
§ 2.5 The Frobenius Method 20
§ 2.6 Fuchsian Equations 24
Chapter 3 The Riemann and Riemann Hilbert Problems 27
§ 3.1 Statement of the Problems 27
§ 3.2 An Observation 28
§ 3.3 The Solution of the Riemann Problem 29
§ 3.4 Apparent Singularities 29
§ 3.5 A Solution of the Riemann Hilbert Problem 30
§ 3.6 Isomonodromic Deformations 35
Chapter 4 Schwarzian Derivatives I 38
§ 4.1 Definitions and Properties 38
§ 4.2 Relations With Differential Equations 39
VI
§ 4.3 A Canonical Form of Differential Equations 42
§ 4.4 Local Behaviour of Schwarzian Derivative 44
Chapter 5 The Gauss Schwarz Theory for Hypergeometric
Differential Equations 46
§ 5.1 Orbifolds and Their Uniformizations 46
§ 5.2 Uniformizing Differential Equations 48
§ 5.3 The Gauss Schwarz Theory 51
Part II
Chapter 6 Hypergeometric Differential Equations in
Several Variables 58
§ 6.1 Hypergeometric Series 58
§ 6.2 Hypergeometric Differential Equations 60
§ 6.3 Contiguity Relations 63
§ 6.4 Euler s Integral Representations 65
§ 6.5 The Erdelyi Takano Integral Representations ....78
§ 6.6 The Barnes Integral Representations 78
§ 6.7 A Relation Between the Equation ¥„ and
the Gamier System G., 79
§ 6.8 Confluent Hypergeometric Equations 81
Chapter 7 The General Theory of Differential Equations ...82
§ 7.1 Singularities of Differential Equations 82
§ 7.2 Holonomic Systems 85
§ 7.3 The Equation F1 89
§ 7.4 Equation of Rank n+1 90
§ 7.5 Differential Equations on Manifolds 92
§ 7.6 Regular Singularities 93
Chapter 8 Schwarzian Derivatives II 95
§ 8.1 Definitions and Properties 95
§ 8.2 Relations With Differential Equations 99
§ 8.3 A Canonical Form of Differential Equations ....100
§ 8.4 Projective Equations and Projective
Connections 102
§ 8.5 Local Properties of Schwarzian Derivatives ....104
VII
Chapter 9 The Riemann and Riemann Hilbert Problems II ..107
§ 9.1 The Riemann Problem in Several Variables 107
§ 9.2 Accessory Parameters 110
Chapter 10 The Gauss Schwarz Theory in Two Variables 115
§ 10.1 Uniformizability of Orbifolds 116
§ 10.2 Orbifolds Whose Universal Uniformizations
Are Symmetric Spaces 118
§ 10.3 Line Arrangements in P7 and Orbifolds
Uniformized by B7 124
§ 10.4 Uniformizing Differential Equations 135
§ 10.5 The Gauss Schwarz Theory for Appell s
Equation F. 137
§ 10.6 The Monodromy Representation of Appell s
Equation F. 145
Chapter 11 Reflection Groups 154
§ 11.1 Unitary Reflection Groups 155
§ 11.2 Unitary Reflection Groups of Dimension 2 159
§ 11.3 Parabolic Reflection Groups of Dimension 2 ....170
§ 11.4 Line Arrangements Defined by Unitary
Reflection Groups of Dimensions 3 and 4 179
Chapter 12 Toward Finding New Differential Equations 181
§ 12.1 Tensor Forms Associated to the Differential
Equations 181
§ 12.2 Integrability Conditions 185
§ 12.3 The Restricted Riemann Problem 188
§ 12.4 G Invariant Differential Equations I 191
§ 12.5 G Invariant Differential Equations II 198
References 2 04
Sources of Figures 215
|
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| indexdate | 2024-07-09T15:42:01Z |
| institution | BVB |
| isbn | 3528089717 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001447716 |
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| physical | XIV, 214 S. graph. Darst. |
| publishDate | 1987 |
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| publisher | Vieweg |
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| series2 | Aspects of mathematics / E. |
| spelling | Yoshida, Masaaki Verfasser aut Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory Braunschweig u.a. Vieweg 1987 XIV, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aspects of mathematics / E. 11. Literaturaturverz. S. 204 - 214 Differential equations, Linear Differential equations, Partial Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd rswk-swf Fuchs-Differentialgleichung (DE-588)4155564-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Hypergeometrische Differentialgleichung (DE-588)4261657-8 s DE-604 Fuchs-Differentialgleichung (DE-588)4155564-8 s Partielle Differentialgleichung (DE-588)4044779-0 s E. Aspects of mathematics 11. (DE-604)BV000018737 11. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001447716&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yoshida, Masaaki Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory Differential equations, Linear Differential equations, Partial Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd Fuchs-Differentialgleichung (DE-588)4155564-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4261657-8 (DE-588)4155564-8 (DE-588)4044779-0 |
| title | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_auth | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_exact_search | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_full | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_fullStr | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_full_unstemmed | Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory |
| title_short | Fuchsian differential equations |
| title_sort | fuchsian differential equations with special emphasis on the gauss schwarz theory |
| title_sub | with special emphasis on the Gauss-Schwarz theory |
| topic | Differential equations, Linear Differential equations, Partial Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd Fuchs-Differentialgleichung (DE-588)4155564-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Linear Differential equations, Partial Hypergeometrische Differentialgleichung Fuchs-Differentialgleichung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001447716&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018737 |
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