Holomorphic Functions, Domains of Holomorphy and Local Properties
Author:
Publisher: Elsevier
Published: 2011-08-26
Total Pages: 131
ISBN-13: 0080871127
DOWNLOAD EBOOKHolomorphic Functions, Domains of Holomorphy and Local Properties
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Author:
Publisher: Elsevier
Published: 2011-08-26
Total Pages: 131
ISBN-13: 0080871127
DOWNLOAD EBOOKHolomorphic Functions, Domains of Holomorphy and Local Properties
Author: Leopoldo Nachbin
Publisher:
Published: 1972
Total Pages: 122
ISBN-13: 9780318397108
DOWNLOAD EBOOKAuthor: Leopoldo Nachbin
Publisher:
Published: 1972
Total Pages: 121
ISBN-13:
DOWNLOAD EBOOKAuthor: Leopoldo Nachbin
Publisher:
Published: 1970
Total Pages: 130
ISBN-13: 9780608159942
DOWNLOAD EBOOKAuthor: R. Michael Range
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 405
ISBN-13: 1475719183
DOWNLOAD EBOOKThe 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.
Author: Leopoldo Nachbin
Publisher:
Published: 1970
Total Pages: 122
ISBN-13:
DOWNLOAD EBOOKAuthor: J.A. Barroso
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 321
ISBN-13: 0080872174
DOWNLOAD EBOOKThis book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.Infinite dimensional Holomorphy appears as a theory rich in fascinating problems and rich in applications to other branches of Mathematics and Mathematical Physics.
Author: Marek Jarnicki
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-05-05
Total Pages: 586
ISBN-13: 3110630273
DOWNLOAD EBOOKThis second extended edition of the classic reference on the extension problem of holomorphic functions in pluricomplex analysis contains a wealth of additional material, organized under the original chapter structure, and covers in a self-contained way all new and recent developments and theorems that appeared since the publication of the first edition about twenty years ago.
Author: R.C. Gunning
Publisher: CRC Press
Published: 1990-05-01
Total Pages: 228
ISBN-13: 9780534133085
DOWNLOAD EBOOKIntroduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
Author: Volker Scheidemann
Publisher: Springer Nature
Published: 2023
Total Pages: 239
ISBN-13: 3031264282
DOWNLOAD EBOOKThis book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.