Function Theory in the Unit Ball of ℂn:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1980
|
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
241 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction |
| Physical Description: | 1 Online-Ressource (XIII, 438 p) |
| ISBN: | 9781461380986 9781461381006 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-1-4613-8098-6 |
Staff View
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| id | DE-604.BV042420660 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461380986 9781461381006 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856077 |
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| physical | 1 Online-Ressource (XIII, 438 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Rudin, Walter Verfasser aut Function Theory in the Unit Ball of ℂn by Walter Rudin New York, NY Springer New York 1980 1 Online-Ressource (XIII, 438 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 241 0072-7830 Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction Mathematics Global analysis (Mathematics) Analysis Mathematik https://doi.org/10.1007/978-1-4613-8098-6 Verlag Volltext |
| spellingShingle | Rudin, Walter Function Theory in the Unit Ball of ℂn Mathematics Global analysis (Mathematics) Analysis Mathematik |
| title | Function Theory in the Unit Ball of ℂn |
| title_auth | Function Theory in the Unit Ball of ℂn |
| title_exact_search | Function Theory in the Unit Ball of ℂn |
| title_full | Function Theory in the Unit Ball of ℂn by Walter Rudin |
| title_fullStr | Function Theory in the Unit Ball of ℂn by Walter Rudin |
| title_full_unstemmed | Function Theory in the Unit Ball of ℂn by Walter Rudin |
| title_short | Function Theory in the Unit Ball of ℂn |
| title_sort | function theory in the unit ball of ℂn |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| url | https://doi.org/10.1007/978-1-4613-8098-6 |
| work_keys_str_mv | AT rudinwalter functiontheoryintheunitballofcn |