Boundary Behaviour of Holomorphic Functions on Bounded Symmetric Domains
Author: A. Koranyi
Publisher:
Published: 1975
Total Pages: 7
ISBN-13:
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Author: A. Koranyi
Publisher:
Published: 1975
Total Pages: 7
ISBN-13:
DOWNLOAD EBOOKAuthor: Elias M. Stein
Publisher: Princeton University Press
Published: 2015-03-08
Total Pages: 83
ISBN-13: 1400871263
DOWNLOAD EBOOKThis book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Kyong Taik Hahn
Publisher:
Published: 1993
Total Pages: 120
ISBN-13:
DOWNLOAD EBOOKAuthor: Wu-Young Chen
Publisher:
Published: 1977
Total Pages: 188
ISBN-13:
DOWNLOAD EBOOKAuthor: E. Vesentini
Publisher: Springer Science & Business Media
Published: 2011-06-08
Total Pages: 297
ISBN-13: 3642110606
DOWNLOAD EBOOKS.G. Gindikin, I.I. Pjateckii-Sapiro, E.B. Vinberg: Homogeneous Kähler manifolds.- S.G. Greenfield: Extendibility properties of real submanifolds of Cn.- W. Kaup: Holomorphische Abbildungen in Hyperbolische Räume.- A. Koranyi: Holomorphic and harmonic functions on bounded symmetric domains.- J.L. Koszul: Formes harmoniques vectorielles sur les espaces localement symétriques.- S. Murakami: Plongements holomorphes de domaines symétriques.- E.M. Stein: The analogues of Fatous’s theorem and estimates for maximal functions.
Author: G.M. Khenkin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 267
ISBN-13: 3642578829
DOWNLOAD EBOOKPlurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.
Author: Raymond O'Neil Wells
Publisher: American Mathematical Soc.
Published: 1977
Total Pages: 342
ISBN-13: 082180250X
DOWNLOAD EBOOKContains sections on Non compact complex manifolds, Differential geometry and complex analysis, Problems in approximation, Value distribution theory, Group representation and harmonic analysis, and Survey papers.
Author: 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: Ichiro Satake
Publisher: Princeton University Press
Published: 2014-07-14
Total Pages: 340
ISBN-13: 1400856809
DOWNLOAD EBOOKThis book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Hyungwoon Koo
Publisher:
Published: 1993
Total Pages: 130
ISBN-13:
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