Several complex variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1967
|
| Edition: | 5. print. |
| Series: | Princeton mathematical series
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 216 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Several complex variables |c Salomon Bochner ; William Ted Martin |
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| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1967 | |
| 300 | |a IX, 216 S. | ||
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| 650 | 0 | 7 | |a Komplexe Variable |0 (DE-588)4164905-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804121242775584768 |
|---|---|
| adam_text | Contents
Preface v
Chapter I. Groups of Transformations by Formal Power-
Series
1. Calculus of formal power-series 3
2. A theorem concerning the circular group 10
3. Topology of formal power-series 11
4. A uniqueness theorem of Henri Cartan 13
5. Bounded groups of linear transformations 16
6. Bounded groups of transformations. A generalization of Cartan s
uniqueness theorem 19
7. A theorem of Behnke and Peschl 23
References 27
Chapter II. Basic Facts about Analytic Functions of Real
and Complex Variables
1. Functions of complex variables 30
2. Functions of real variables 33
3. Functions of mixed variables 35
4. Conjugate complex variables 36
5. Majorized families of functions 40
6. A theorem of E. E. Levi 41
References 43
Chapter III. Analytic Mappings with a Fixed Point
1. Analytic homeomorphisms of the entire space into a part of itself. . . 45
2. The uniqueness theorem of H. Cartan 48
3. Criterion for a transformation with a fixed point to be an automorphism 50
4. Groups of automorphisms with fixed point 53
5. Analytic mapping of spherical surfaces onto each other 55
6. Schwarz s lemma and the Hadamard three-spheres theorem 59
References 62
Chapter IV. Analytic Completion
1. Preliminaries 66
2. Theorems on completion 68
3. Convex domains 70
4. Modified convexity 72
5. Maximal domains 75
6. Radiated domains 75
7. Domains of circular type 78
8. Domains of multi-circular type 81
vii
viii CONTENTS
9. Some concluding remarks 82
References 82
Chapter V. Singularities at Boundary Points
1. Unbounded functions 84
2. An analytic criterion for completion 86
3. Relative completion 89
4. Convex tubes 90
5. Analytic functions in elliptical polycylinders 92
6. Completion of tubes. A special case 96
7. The general case 97
References 102
Chapter VI. Inequalities, Bounds and Norms
1. Inequality of Jensen-Hartogs 103
2. Maximum on the boundary 107
3. Approximations 109
4. Bounded functions in tubes 113
5. Lp- norm for volume integrals 116
6. Orthogonal systems 121
7. Surface integrals 124
8. Multiple Fourier integrals 128
9. Functions of integrable square 130
References 132
Chapter VII. The Theory of Hartogs. Subharmonic
Functions
1. Harnack s theorem 135
2. Hartogs main theorem 137
3. Contribution of Osgood 139
4. Hartogs theorem on analyticity in each variable 140
5. Extension of Hartogs main theorem 141
6. Hartogs domains and subharmonic functions 142
7. Generalized Hartogs domains 145
8. Half-planes instead of circles 147
9. Borel radii 148
10. Radius of meromorphy 151
11. A theorem on complex Lie groups 154
References 156
Chapter VIII. Removable Singularities
1. Generalized solutions of partial differential equations 158
2. Constant coefficients 161
3. Harmonic functions 162
4. Systems of equations and of functions 164
5. Nullifies 166
6. Removable singularities in general 168
7. Removable singularities of analytic functions 169
CONTENTS ix
8. A type of exceptional set 171
9. A basic theorem on removable singularities 173
10. On Jacobians 179
References 182
Chapter IX. Algebraic Theorems
1. The Weierstrass preparation theorem 183
2. Distinguished polynomials 190
3. Characteristic manifolds 194
4. A remark on algebraic functions 198
5. Rational and algebraic functions on products of domains ... 199
References 203
Chapter X. Local Analytic Varieties
1. Introduction. The basic condition 204
2 Analytic manifolds at a point 205
3. Irreducible manifolds 206
Index 213
|
| any_adam_object | 1 |
| author | Bochner, S. 1899-1982 Martin, William Ted |
| author_GND | (DE-588)119439131 |
| author_facet | Bochner, S. 1899-1982 Martin, William Ted |
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| author_sort | Bochner, S. 1899-1982 |
| author_variant | s b sb w t m wt wtm |
| building | Verbundindex |
| bvnumber | BV007066719 |
| classification_rvk | SK 780 |
| ctrlnum | (OCoLC)258039110 (DE-599)BVBBV007066719 |
| discipline | Mathematik |
| edition | 5. print. |
| format | Book |
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| id | DE-604.BV007066719 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:54:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004489933 |
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| physical | IX, 216 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Princeton mathematical series |
| series2 | Princeton mathematical series |
| spelling | Bochner, S. 1899-1982 Verfasser (DE-588)119439131 aut Several complex variables Salomon Bochner ; William Ted Martin 5. print. Princeton, NJ Princeton Univ. Press 1967 IX, 216 S. txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 10 Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 s DE-604 Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Martin, William Ted Verfasser aut Princeton mathematical series 10 (DE-604)BV000019035 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004489933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bochner, S. 1899-1982 Martin, William Ted Several complex variables Princeton mathematical series Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4277015-4 (DE-588)4018935-1 (DE-588)4164905-9 |
| title | Several complex variables |
| title_auth | Several complex variables |
| title_exact_search | Several complex variables |
| title_full | Several complex variables Salomon Bochner ; William Ted Martin |
| title_fullStr | Several complex variables Salomon Bochner ; William Ted Martin |
| title_full_unstemmed | Several complex variables Salomon Bochner ; William Ted Martin |
| title_short | Several complex variables |
| title_sort | several complex variables |
| topic | Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | Mehrere Variable Funktionentheorie Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004489933&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000019035 |
| work_keys_str_mv | AT bochners severalcomplexvariables AT martinwilliamted severalcomplexvariables |