An introduction to several complex variables and partial differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman
1997
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 454 S. Ill., graph. Darst. |
| ISBN: | 0582255007 |
Staff View
MARC
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| 100 | 1 | |a Begehr, Heinrich G. W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to several complex variables and partial differential equations |c Heinrich G W Begehr and Abduhamid Dzhuraev |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman |c 1997 | |
| 300 | |a 454 S. |b Ill., graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 88 | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Functions of several complex variables | |
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Record in the Search Index
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|---|---|
| adam_text | Table of contents
1 Elementary properties of holomorphic functions 1
1.1 Holomorphic functions 1
1.1.1 Basic concepts 1
1.1.2 Local properties of holomorphic functions 6
1.1.3 Hartogs theorem 7
1.2 Some integrals over spheres 8
1.3 Automorphisms 12
1.3.1 Holomorphic mappings 12
1.3.2 Automorphisms of the unit ball 16
1.3.3 Wedges 19
1.4 Integral representations 20
1.5 Analytic varieties 29
1.5.1 Zero sets of analytic functions 29
1.5.2 Analytic subvarieties 32
2 Generalizations of the Cauchy—Pompeiu formula
and the 5 problem 36
2.1 Differential forms 36
2.1.1 Real forms 36
2.1.2 Complex forms 40
2.2 Differentiation of integrals with weak singularities 42
2.2.1 Integrals in real spaces 42
2.2.2 Integrals in complex spaces 44
2.3 The 9 problem with compact support and further preparation 48
2.3.1 3 problem with compact support 48
2.3.2 Particular complex differential forms 51
2.4 The Bochner Martinelli formula and other generalizations
of the Cauchy Pompeiu formula 55
2.5 The d problem in convex domains 60
2.6 Some overdetermined boundary value problems 64
2.6.1 Problems in the unit disc 64
2.6.2 Problems in bounded regions of Wn 67
2.6.3 Canonical kernel function for the unit ball 71
2.7 Tangential Cauchy Riemann operators 77
3 Holomorphic solutions of holomorphic systems
of partial differential equations 84
3.1 Polynomial solutions of a homogeneous equation
with constant coefficients in (P n 84
3.1.1 Equations in W 2 84
3.1.2 First order equations in W n 86
3.2 Structure of solutions of linear first order holomorphic systems
with one unknown function 88
3.2.1 A first order system of n — 1 equations in W n 88
3.2.2 A first order system of p equations in W n 91
3.2.3 General first order system of n — 1 equations 93
3.3 Structure of holomorphic solutions of higher order linear
holomorphic equations in W 2 99
3.3.1 Second order equations in W2 100
3.3.2 General equations in W 2 107
3.4 Boundary value problems for piecewise holomorphic solutions
of holomorphic equations with one unknown function 110
3.4.1 Some first order systems 110
3.4.2 Higher order systems 116
3.4.3 Second order equations for higher dimensions 125
3.5 Boundary value problems for linear first order holomorphic systems
with several unknown functions in W 2 126
3.6 Linear system of partial differential equations
with analytic coefficients 133
3.6.1 Systems for one unknown 133
3.6.2 Systems for several unknowns 144
4 Boundary value problems for holomorphic functions and
non holomorphic systems in bounded domains of W n 149
4.1 Riemann Hilbert boundary value problem for
holomorphic functions in the unit ball of W 149
4.2 Oblique derivative problems in the unit ball of W 170
4.3 Pluriharmonic, pluriholomorphic and bianalytic functions 176
4.4 Inhomogeneous second order overdetermined elliptic systems 181
4.4.1 Solutions with compact support 181
4.4.2 A boundary value problem for the
inhomogeneous pluriholomorphic equation 184
4.4.3 Inhomogeneous biholomorphic equation in the unit ball 188
4.5 Boundary value problems for inhomogeneous overdetermined
elliptic systems in bounded domains of W n 194
4.5.1 Riemann Hilbert problem for
inhomogeneous Cauchy Riemann systems 195
4.5.2 Riemann Hilbert problem for
general first order overdetermined elliptic systems 202
4.5.3 Boundary value problems for
second order elliptic overdetermined systems 208
4.5.4 Dirichlet problem 219
4.5.5 Neumann problem 225
4.5.6 Applications 235
4.6 Generalization to higher order systems 238
5 Riemann Hilbert boundary value problem for
Cauchy Riemann systems in polydiscs 243
5.1 Schwarz problem for analytic functions 243
5.2 Inhomogeneous Cauchy Riemann system 256
5.3 Dirichlet problem for inhomogeneous pluriharmonic systems 279
5.4 Riemann Hilbert problem for analytic functions 295
5.5 Riemann Hilbert problem for inhomogeneous Cauchy Riemann systems . 303
5.5.1 The problem with non negative multiindex 303
5.5.2 The problem with arbitrary multiindex 333
6 First and second order systems in several
complex unknown functions 366
I. Elliptic systems 366
6.1 Introduction 366
6.1.1 First order elliptic systems 366
6.1.2 Second order elliptic systems 368
6.2 Dirichlet problem for first order elliptic systems 372
6.3 Second order elliptic systems 387
6.4 Dirichlet problem for Beltrami systems in W n 394
6.5 Boundary value problems for second order
overdetermined elliptic system 397
II. Complex analysis of some non elliptic systems 402
6.6 Systems having real characteristics 402
6.7 Systems without real characteristics 409
6.8 Overdetermined systems possessing real characteristics 425
6.8.1 First order systems 425
6.8.2 Second order systems 430
• Table of notation 438
• Bibliography 440
• Index 448
|
| any_adam_object | 1 |
| author | Begehr, Heinrich G. W. Džuraev, Abduchamid 1932- |
| author_GND | (DE-588)172051576 |
| author_facet | Begehr, Heinrich G. W. Džuraev, Abduchamid 1932- |
| author_role | aut aut |
| author_sort | Begehr, Heinrich G. W. |
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| building | Verbundindex |
| bvnumber | BV011530884 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.7 |
| callnumber-search | QA331.7 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 780 |
| ctrlnum | (OCoLC)32699060 (DE-599)BVBBV011530884 |
| dewey-full | 515/.94 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.94 515.353 |
| dewey-search | 515/.94 515.353 |
| dewey-sort | 3515 294 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011530884 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:19Z |
| institution | BVB |
| isbn | 0582255007 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007760596 |
| oclc_num | 32699060 |
| open_access_boolean | |
| owner | DE-739 DE-384 DE-11 DE-188 |
| owner_facet | DE-739 DE-384 DE-11 DE-188 |
| physical | 454 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Longman |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Begehr, Heinrich G. W. Verfasser aut An introduction to several complex variables and partial differential equations Heinrich G W Begehr and Abduhamid Dzhuraev 1. publ. Harlow, Essex Longman 1997 454 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 88 Differential equations, Partial Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere komplexe Variable (DE-588)4169285-8 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Džuraev, Abduchamid 1932- Verfasser (DE-588)172051576 aut Pitman monographs and surveys in pure and applied mathematics 88 (DE-604)BV000022446 88 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007760596&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Begehr, Heinrich G. W. Džuraev, Abduchamid 1932- An introduction to several complex variables and partial differential equations Pitman monographs and surveys in pure and applied mathematics Differential equations, Partial Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4044779-0 (DE-588)4169285-8 |
| title | An introduction to several complex variables and partial differential equations |
| title_auth | An introduction to several complex variables and partial differential equations |
| title_exact_search | An introduction to several complex variables and partial differential equations |
| title_full | An introduction to several complex variables and partial differential equations Heinrich G W Begehr and Abduhamid Dzhuraev |
| title_fullStr | An introduction to several complex variables and partial differential equations Heinrich G W Begehr and Abduhamid Dzhuraev |
| title_full_unstemmed | An introduction to several complex variables and partial differential equations Heinrich G W Begehr and Abduhamid Dzhuraev |
| title_short | An introduction to several complex variables and partial differential equations |
| title_sort | an introduction to several complex variables and partial differential equations |
| topic | Differential equations, Partial Functions of several complex variables Funktionentheorie (DE-588)4018935-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Differential equations, Partial Functions of several complex variables Funktionentheorie Partielle Differentialgleichung Mehrere komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007760596&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
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