Holomorphic Functions and Integral Representations in Several Complex Variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1986
|
| Series: | Graduate Texts in Mathematics
108 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains in C", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particular, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between complex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods |
| Physical Description: | 1 Online-Ressource (XX, 392 p) |
| ISBN: | 9781475719185 9781441930781 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-1918-5 |
Staff View
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| discipline | Mathematik |
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| indexdate | 2024-07-10T01:21:08Z |
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| isbn | 9781475719185 9781441930781 |
| issn | 0072-5285 |
| language | English |
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| spelling | Range, R. Michael Verfasser aut Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range New York, NY Springer New York 1986 1 Online-Ressource (XX, 392 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 108 0072-5285 The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains in C", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particular, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between complex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods Mathematics Global analysis (Mathematics) Analysis Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 s Holomorphe Funktion (DE-588)4025645-5 s Mehrere komplexe Variable (DE-588)4169285-8 s 1\p DE-604 Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s 2\p DE-604 3\p DE-604 4\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 5\p DE-604 Graduate Texts in Mathematics 108 (DE-604)BV035421258 108 https://doi.org/10.1007/978-1-4757-1918-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Range, R. Michael Holomorphic Functions and Integral Representations in Several Complex Variables Graduate Texts in Mathematics Mathematics Global analysis (Mathematics) Analysis Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| subject_GND | (DE-588)4025645-5 (DE-588)4018935-1 (DE-588)4277015-4 (DE-588)4071510-3 (DE-588)4169285-8 (DE-588)4127585-8 |
| title | Holomorphic Functions and Integral Representations in Several Complex Variables |
| title_auth | Holomorphic Functions and Integral Representations in Several Complex Variables |
| title_exact_search | Holomorphic Functions and Integral Representations in Several Complex Variables |
| title_full | Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range |
| title_fullStr | Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range |
| title_full_unstemmed | Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range |
| title_short | Holomorphic Functions and Integral Representations in Several Complex Variables |
| title_sort | holomorphic functions and integral representations in several complex variables |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Holomorphe Funktion Funktionentheorie Mehrere Variable Funktion Mathematik Mehrere komplexe Variable Integraldarstellung |
| url | https://doi.org/10.1007/978-1-4757-1918-5 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT rangermichael holomorphicfunctionsandintegralrepresentationsinseveralcomplexvariables |