Fuchsian differential equations: with special emphasis on the Gauss-Schwarz theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Braunschweig u.a.
Vieweg
1987
|
| Schriftenreihe: | Aspects of mathematics / E.
11. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturaturverz. S. 204 - 214 |
| Beschreibung: | XIV, 214 S. graph. Darst. |
| ISBN: | 3528089717 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002203673 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 890928s1987 d||| |||| 00||| eng d | ||
| 020 | |a 3528089717 |9 3-528-08971-7 | ||
| 035 | |a (OCoLC)17344932 | ||
| 035 | |a (DE-599)BVBBV002203673 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-739 |a DE-355 |a DE-824 |a DE-29T |a DE-19 |a DE-706 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA372 | |
| 082 | 0 | |a 515.352 | |
| 082 | 0 | |a 515.353 |b Yo83f | |
| 084 | |a SK 500 |0 (DE-625)143243: |2 rvk | ||
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 750 |0 (DE-625)143254: |2 rvk | ||
| 084 | |a 34A55 |2 msc | ||
| 084 | |a MAT 357f |2 stub | ||
| 084 | |a MAT 349f |2 stub | ||
| 084 | |a 35Q15 |2 msc | ||
| 084 | |a 30E25 |2 msc | ||
| 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 | |
| 650 | 0 | 7 | |a Hypergeometrische Differentialgleichung |0 (DE-588)4261657-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fuchs-Differentialgleichung |0 (DE-588)4155564-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hypergeometrische Differentialgleichung |0 (DE-588)4261657-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Fuchs-Differentialgleichung |0 (DE-588)4155564-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 810 | 2 | |a E. |t Aspects of mathematics |v 11. |w (DE-604)BV000018737 |9 11. | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001447716 | ||
Datensatz im Suchindex
| _version_ | 1804116658916163584 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Yoshida, Masaaki |
| author_facet | Yoshida, Masaaki |
| author_role | aut |
| author_sort | Yoshida, Masaaki |
| author_variant | m y my |
| building | Verbundindex |
| bvnumber | BV002203673 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 520 SK 540 SK 750 |
| classification_tum | MAT 357f MAT 349f |
| ctrlnum | (OCoLC)17344932 (DE-599)BVBBV002203673 |
| dewey-full | 515.352 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 515.353 |
| dewey-search | 515.352 515.353 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02261nam a2200577 cb4500</leader><controlfield tag="001">BV002203673</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1987 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3528089717</subfield><subfield code="9">3-528-08971-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)17344932</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002203673</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA372</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.352</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.353</subfield><subfield code="b">Yo83f</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 500</subfield><subfield code="0">(DE-625)143243:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 750</subfield><subfield code="0">(DE-625)143254:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">34A55</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 357f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 349f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35Q15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">30E25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yoshida, Masaaki</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fuchsian differential equations</subfield><subfield code="b">with special emphasis on the Gauss-Schwarz theory</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Braunschweig u.a.</subfield><subfield code="b">Vieweg</subfield><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 214 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Aspects of mathematics / E.</subfield><subfield code="v">11.</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturaturverz. S. 204 - 214</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Linear</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Partial</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hypergeometrische Differentialgleichung</subfield><subfield code="0">(DE-588)4261657-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fuchs-Differentialgleichung</subfield><subfield code="0">(DE-588)4155564-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hypergeometrische Differentialgleichung</subfield><subfield code="0">(DE-588)4261657-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Fuchs-Differentialgleichung</subfield><subfield code="0">(DE-588)4155564-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">E.</subfield><subfield code="t">Aspects of mathematics</subfield><subfield code="v">11.</subfield><subfield code="w">(DE-604)BV000018737</subfield><subfield code="9">11.</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001447716</subfield></datafield></record></collection> |
| id | DE-604.BV002203673 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:01Z |
| institution | BVB |
| isbn | 3528089717 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001447716 |
| oclc_num | 17344932 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| physical | XIV, 214 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Vieweg |
| record_format | marc |
| 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 |
| work_keys_str_mv | AT yoshidamasaaki fuchsiandifferentialequationswithspecialemphasisonthegaussschwarztheory |