Boundary Behavior of Holomorphic Functions on Domains of Finite Type
Author: Hyungwoon Koo
Publisher:
Published: 1993
Total Pages: 130
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Hyungwoon Koo
Publisher:
Published: 1993
Total Pages: 130
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: 康素珍
Publisher:
Published: 1986
Total Pages: 78
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: David W. Catlin
Publisher:
Published: 1978
Total Pages: 176
ISBN-13:
DOWNLOAD EBOOKAuthor: Steven G. Krantz
Publisher: Springer Science & Business Media
Published: 2009-05-24
Total Pages: 367
ISBN-13: 0817646698
DOWNLOAD EBOOKThis self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Author: N Kono
Publisher: World Scientific
Published: 1999-10-19
Total Pages: 322
ISBN-13: 9814543527
DOWNLOAD EBOOKThis proceedings volume reflects the current interest in and future direction of probability theory and related theory of analysis and statistics. It contains 2 survey papers and 21 contributed papers.
Author: Jeffery D. McNeal
Publisher: American Mathematical Soc.
Published: 2010-01-01
Total Pages: 601
ISBN-13: 0821872753
DOWNLOAD EBOOK"Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description.
Author: John Bland
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 338
ISBN-13: 0821832735
DOWNLOAD EBOOKThis book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Author: Elias M. Stein
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 435
ISBN-13: 1400882095
DOWNLOAD EBOOKBased on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.