Behavior of Holomorphic Functions at Generating Submanifolds of the Boundary
Author: Vivian Susan Klein
Publisher:
Published: 1979
Total Pages: 192
ISBN-13:
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Author: Vivian Susan Klein
Publisher:
Published: 1979
Total Pages: 192
ISBN-13:
DOWNLOAD EBOOKAuthor: Wade C. Ramey
Publisher:
Published: 1981
Total Pages: 126
ISBN-13:
DOWNLOAD EBOOKAuthor: Hyungwoon Koo
Publisher:
Published: 1993
Total Pages: 130
ISBN-13:
DOWNLOAD EBOOKAuthor: Fausto Di Biase
Publisher: Birkhauser
Published: 2006-10
Total Pages: 300
ISBN-13: 9780817642990
DOWNLOAD EBOOKThis monograph examines the boundary behavior of holomorphic functions in several complex variables. Moving beyond the early ideas of Fatou and others, Koranyi and then Stein in the late 1960s and early 1970s deepened the study of Fatou-type theorems in several complex variables, showing that in a general context, approach regions of a shape dramatically larger than non-tangential will give rise to a Fatou-type theorem. These have become known as the admissible regions of Koranyi and Stein. It turns out, however, that the admissible approach regions are only optimal on strongly pseudoconvex domains. Considerable effort has been made in the last 20 years to adapt Fatou theory, and the approach regions in particular, to the Levi geometry of a given domain in multidimensional complex space. The work of Di Biase in the late 1990s is devoted to the Nagel--Stein phenomenon, describing a more general notion of approach region that supersedes the classical ideas of non-tangential and admissible. Krantz's work Function Theory of Several Complex Variables (2000), still the only introduction to the subject, focuses on methods based on maximal function estimates. To date, the main open problem, which is the special focus of this book, is the issue of determining the {it optimal natural approach regions} for the almost everywhere convergence to the boundary of certain smoothly bounded pseudoconvex domains. This book provides the proper framework for the eventual solution of the main problem. This work gives an updated, comprehensive, and self-contained exposition of many results that have never appeared in book form. Starting with foundational material, i.e., from the unit disc in one complexvariable, the reader is lead to the latest discoveries in higher dimensions. New results in boundary value issues of holomorphic functions are examined, which in turn point to new open problems. The book may be used by analysts for individual study or by graduate students.
Author: Manuel Elgueta
Publisher:
Published: 1975
Total Pages: 106
ISBN-13:
DOWNLOAD EBOOKAuthor: Paula A. Russo
Publisher:
Published: 1984
Total Pages: 170
ISBN-13:
DOWNLOAD EBOOKAuthor: 康素珍
Publisher:
Published: 1986
Total Pages: 78
ISBN-13:
DOWNLOAD EBOOKAuthor: Sergey Pinchuk
Publisher: Springer Nature
Published: 2023-10-16
Total Pages: 217
ISBN-13: 3031371496
DOWNLOAD EBOOKThis monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle. Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
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:
Publisher:
Published: 1989
Total Pages: 1016
ISBN-13:
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