Integral representations and residues in multidimensional complex analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
1983
|
| Schriftenreihe: | Translations of mathematical monographs
58 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize <engl.>. - Aus d. Russ. übers. |
| Beschreibung: | X, 283 S. |
| ISBN: | 082184511X |
Internformat
MARC
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| 240 | 1 | 0 | |a Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize |
| 245 | 1 | 0 | |a Integral representations and residues in multidimensional complex analysis |c by I. A. Aǐzenberg ; A. P. Yuzhakov |
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 1983 | |
| 300 | |a X, 283 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 58 | |
| 500 | |a EST: Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize <engl.>. - Aus d. Russ. übers. | ||
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| 689 | 0 | 2 | |a Integraldarstellung |0 (DE-588)4127585-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804114815805816832 |
|---|---|
| adam_text | Table of Contents
Preface vii
Preliminaries 1
CHAPTER I. Integral Representations and the Logarithmic Residue 15
1. The Martinelli Bochner integral representation 15
2. Multiplicity of a zero of a holomorphic mapping. The Rouche
principle 18
3. The fundamental integral formula of Leray and Koppelman 25
4. The Cauchy formula. The logarithmic residue with respect to
the skeleton 30
5. The Andreotti Norguet formula and generalizations of it 38
6. The Bergman kernel function, the Szego kernel, and integral
representations with a holomorphic kernel on the Shilov bound¬
ary 42
7. The Martinelli Bochner Koppelman integral representation for
exterior differential forms 49
CHAPTER II. Integral Representations of Special Form for Holomor¬
phic Functions 59
8. Modifications and the simplest particular cases of the Leray
formula 59
9. The Bergman Weil formula 65
10. Integral representation for strictly pseudoconvex domains 66
11. Integral formulas for functions holomorphic in n circular do¬
mains 73
12. The Schwarz kernel and integral representations of holomorphic
functions with nonnegative real part 80
CHAPTER m. The Theory of Residues 93
13. Statement of the problem 93
14. Application of Alexander Pontryagin duality 94
15. Application of de Rham duality 98
v
vi CONTENTS
16. The Leray theory of residues 101
17. Cohomological reduction of certain semimeromorphic and ra¬
tional forms 113
18. Residues of rational functions of two variables 119
19. Local residues of certain meromorphic and rational functions in
Cn 129
CHAPTER IV. Applications to Implicit Functions, Systems of Non¬
linear Equations, Computation of the Multiplicity of a Zero, and
Combinatorics 137
20. Expansion of implicit functions in power series and function
series 137
21. Application of the multidimensional logarithmic residue to sys¬
tems of nonlinear equations 157
22. Computation of the multiplicity of a zero of a system of holomor
phic functions from their Taylor series 175
23. Application of multiple residues for finding generating functions
and computing combinatorial sums 188
CHAPTER V. Some Applications in Multidimensional Complex
Analysis 195
24. The Hartogs Bochner theorem on necessary analytic extension.
Approximation of holomorphic functions on Weil polyhedra and
linearly convex compact sets 195
25. The 3 problem and Oka s theorems 204
26. Forms orthogonal to holomorphic functions. Lewy s equation.
General form of integral representation formulas for holomor¬
phic functions 219
27. A basis in the space of holomorphic functions with fixed al¬
gebraic singularities 241
Brief historical notes 249
Bibliography 259
Subject index 279
Index of notation 283
|
| any_adam_object | 1 |
| author | Ajzenberg, Lev Abramovič 1937- Južakov, Aleksandr P. |
| author_GND | (DE-588)121563545 |
| author_facet | Ajzenberg, Lev Abramovič 1937- Južakov, Aleksandr P. |
| author_role | aut aut |
| author_sort | Ajzenberg, Lev Abramovič 1937- |
| author_variant | l a a la laa a p j ap apj |
| building | Verbundindex |
| bvnumber | BV000348585 |
| classification_rvk | SK 780 |
| classification_tum | MAT 320f |
| ctrlnum | (OCoLC)476233333 (DE-599)BVBBV000348585 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Residuentheorie gnd |
| genre_facet | Residuentheorie |
| id | DE-604.BV000348585 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:12:43Z |
| institution | BVB |
| isbn | 082184511X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000216725 |
| oclc_num | 476233333 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-739 DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-384 DE-83 DE-188 |
| physical | X, 283 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Ajzenberg, Lev Abramovič 1937- Verfasser (DE-588)121563545 aut Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize Integral representations and residues in multidimensional complex analysis by I. A. Aǐzenberg ; A. P. Yuzhakov Providence, RI American Mathematical Soc. 1983 X, 283 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 58 EST: Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize <engl.>. - Aus d. Russ. übers. Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Residuentheorie gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 s Residuentheorie f Integraldarstellung (DE-588)4127585-8 s DE-604 Južakov, Aleksandr P. Verfasser aut Translations of mathematical monographs 58 (DE-604)BV000002394 58 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000216725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ajzenberg, Lev Abramovič 1937- Južakov, Aleksandr P. Integral representations and residues in multidimensional complex analysis Translations of mathematical monographs Holomorphe Funktion (DE-588)4025645-5 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| subject_GND | (DE-588)4025645-5 (DE-588)4127585-8 |
| title | Integral representations and residues in multidimensional complex analysis |
| title_alt | Integral'nye predstavlenija i vyčety v mnogomernom kompleksnom analize |
| title_auth | Integral representations and residues in multidimensional complex analysis |
| title_exact_search | Integral representations and residues in multidimensional complex analysis |
| title_full | Integral representations and residues in multidimensional complex analysis by I. A. Aǐzenberg ; A. P. Yuzhakov |
| title_fullStr | Integral representations and residues in multidimensional complex analysis by I. A. Aǐzenberg ; A. P. Yuzhakov |
| title_full_unstemmed | Integral representations and residues in multidimensional complex analysis by I. A. Aǐzenberg ; A. P. Yuzhakov |
| title_short | Integral representations and residues in multidimensional complex analysis |
| title_sort | integral representations and residues in multidimensional complex analysis |
| topic | Holomorphe Funktion (DE-588)4025645-5 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| topic_facet | Holomorphe Funktion Integraldarstellung Residuentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000216725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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