Holomorphic Functions and Integral Representations in Several Complex Variab...
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Holomorphic Functions and Integral Representation
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Lieu où se trouve l'objet : Interlochen, Michigan, États-Unis
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Numéro de l'objet eBay :126809608432
Dernière mise à jour le 23 mai 2025 17:37:58 CEST. Afficher toutes les modificationsAfficher toutes les modifications
Caractéristiques de l'objet
- État
- Release Year
- 1986
- Book Title
- Holomorphic Functions and Integral Representations in Several ...
- ISBN
- 9780387962597
À propos de ce produit
Product Identifiers
Publisher
Springer New York
ISBN-10
038796259X
ISBN-13
9780387962597
eBay Product ID (ePID)
14038282857
Product Key Features
Number of Pages
Xx, 392 Pages
Publication Name
Holomorphic Functions and Integral Representations in Several Complex Variables
Language
English
Publication Year
1986
Subject
Functional Analysis, Mathematical Analysis, Complex Analysis
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
58.9 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
85-030309
Dewey Edition
22
Series Volume Number
108
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515.98
Table Of Content
I Elementary Local Properties of Holomorphic Functions.- II Domains of Holomorphy and Pseudoconvexity.- III Differential Forms and Hermitian Geometry.- IV Integral Representations in ?n.- V The Levi Problem and the Solution of ? on Strictly Pseudoconvex Domains.- VI Function Theory on Domains of Holomorphy in ?n.- VII Topics in Function Theory on Strictly Pseudoconvex Domains.- Appendix A.- Appendix B.- Appendix C.- Glossary of Symbols and Notations.
Synopsis
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 inC", 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 particu lar, 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 differ ential 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 com plex 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., This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional theory such as pseudoconvexity and holomorphic convexity, and leads up to complete proofs of fundamental global results, both classical and new., 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 inC", 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 particu- lar, 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 differ- ential 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 com- plex 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.
LC Classification Number
QA299.6-433
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