Integrals of Cauchy type on the ball:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Cambridge, MA [u.a.]
International Press
1993
|
| Series: | Monographs in analysis
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | III, 304 S. |
| ISBN: | 1571460055 |
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MARC
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| 100 | 1 | |a Gong, Sheng |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integrals of Cauchy type on the ball |c Sheng Gong |
| 264 | 1 | |a Cambridge, MA [u.a.] |b International Press |c 1993 | |
| 300 | |a III, 304 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
INTRODUCTION 1
0.1 Introduction 1
0.2 The Cauchy Szego Kernel 3
0.3 The Cauchy Fantappie Kernel 10
0.4 The Henkin Ramirez Kernel and The Stein Kerzman Kernel 13
I INTEGRALS OF CAUCHY TYPE ON THE BALL 19
1.1 Introduction 19
1.2 A Lemma 20
1.3 Cauchy Principal Value 27
1.4 Limits of Integral of Cauchy Type 30
1.5 Continuity of The Limit Function of Integral of Cauchy Type 34
1.6 Extension of Theorem 1.4.2 39
1.7 Proof of Lemma 1.6.1 41
1.8 Another Cauchy Principal Value 54
1.9 The Proof of Lemma 1.8.1 55
1.10 K limits 64
II SINGULAR INTEGRAL EQUATIONS ON THE COM¬
PLEX SPHERE 69
2.1 Introduction 69
2.2 Composite Singular Integral Formula with the Cauchy Kernel 70
2.3 B and h kernels, B type and h type Integrals 74
2.4 Composite Singular Integral Formulas with the h kernel ... 80
2.5 Operators H, B and h 85
2.6 Singular Integral Equations with Cauchy Kernel 88
2.7 Singular Integral Equations with B and h Kernels 91
2.8 Some Exceptional Cases 94
2.9 Singular Integral Equations with B and h Kernels (continued) 97
2.10 Systems of Singular Integral Equations with Cauchy Kernel . 99
ii CONTENTS
2.11 Systems of Singular Integral Equations with B and h Kernels 100
2.12 Singular Integral Equations with Variable Coefficients on the
Complex Sphere 106
2.13 Formulae for Substitution 125
2.14 Regularizations 136
2.15 Direct Solution of Some Equations 140
IIIHADAMARD PRINCIPAL VALUE ON THE COMPLEX
SPHERE 147
3.1 Introduction 147
3.2 Some Lemmas 149
3.3 Hadamard Principal Value 158
3.4 Plemelj Formula with Hadamard Principal Value 164
3.5 Derivatives of Integral of Cauchy Type on the Complex Sphere 166
3.6 Limiting Values at Some Special Points 174
3.7 Representing Boundary Values by Hadamard Principal Value 177
IV INTEGRALS OF CAUCHY TYPE ON HYPERBOLIC
SPACE OF LIE SPHERES 197
4.1 Introduction 197
4.2 Two Lemmas 199
4.3 The Cauchy Principal Value on BIV Civ 207
4.4 Limiting Values on Biv — Civ of Integral of Cauchy Type . . 217
4.5 The Boundary Values of B Harmonic Functions 224
4.6 Limiting Values on Civ of Integral of Cauchy Type 226
V INTEGRALS OF CAUCHY TYPE ON HYPERBOLIC
SPACE OF MATRICES 243
5.1 Introduction 243
5.2 Limiting Value on Ci(n) of integral of Cauchy type 245
5.3 A Lemma 251
5.4 Limiting Value on Cj~ of Integral of Cauchy Type on
7e/(m,n) 253
5.5 Boundary Behavior of B harmonic Functions in TZi(m,n) . . 262
VI INTEGRALS OF HENKIN TYPE ON STRICTLY
PSEUDOCONVEX DOMAINS 267
6.1 Introduction 267
6.2 A General Plemelj Formula 268
6.3 Singular Integrals on btl 272
CONTENTS iii
6.4 The Ellipse Neighborhood Case 275
6.5 The Rectangle Neighborhood Case 283
6.6 On Bochner Martinelli Integrals 291
REFERENCES 295
NOTATIONS 299
INDEX 301
|
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| id | DE-604.BV011034581 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:02:57Z |
| institution | BVB |
| isbn | 1571460055 |
| language | English Chinese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007389334 |
| oclc_num | 31376904 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-11 |
| owner_facet | DE-384 DE-703 DE-11 |
| physical | III, 304 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | International Press |
| record_format | marc |
| series | Monographs in analysis |
| series2 | Monographs in analysis |
| spelling | Gong, Sheng Verfasser aut Integrals of Cauchy type on the ball Sheng Gong Cambridge, MA [u.a.] International Press 1993 III, 304 S. txt rdacontent n rdamedia nc rdacarrier Monographs in analysis 1 Boule unité ram Cauchy, intégrales de ram Cauchy integrals Unit ball Einheitskugel (DE-588)4151312-5 gnd rswk-swf Cauchy-Integral (DE-588)4511419-5 gnd rswk-swf Cauchy-Integral (DE-588)4511419-5 s Einheitskugel (DE-588)4151312-5 s DE-604 Monographs in analysis 1 (DE-604)BV011034569 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007389334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gong, Sheng Integrals of Cauchy type on the ball Monographs in analysis Boule unité ram Cauchy, intégrales de ram Cauchy integrals Unit ball Einheitskugel (DE-588)4151312-5 gnd Cauchy-Integral (DE-588)4511419-5 gnd |
| subject_GND | (DE-588)4151312-5 (DE-588)4511419-5 |
| title | Integrals of Cauchy type on the ball |
| title_auth | Integrals of Cauchy type on the ball |
| title_exact_search | Integrals of Cauchy type on the ball |
| title_full | Integrals of Cauchy type on the ball Sheng Gong |
| title_fullStr | Integrals of Cauchy type on the ball Sheng Gong |
| title_full_unstemmed | Integrals of Cauchy type on the ball Sheng Gong |
| title_short | Integrals of Cauchy type on the ball |
| title_sort | integrals of cauchy type on the ball |
| topic | Boule unité ram Cauchy, intégrales de ram Cauchy integrals Unit ball Einheitskugel (DE-588)4151312-5 gnd Cauchy-Integral (DE-588)4511419-5 gnd |
| topic_facet | Boule unité Cauchy, intégrales de Cauchy integrals Unit ball Einheitskugel Cauchy-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007389334&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011034569 |
| work_keys_str_mv | AT gongsheng integralsofcauchytypeontheball |