Download or read book Boundary Behavior of Bounded Holomorphic Functions Along Maximally Complex Submanifolds written by Wade C. Ramey and published by . This book was released on 1981 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary Behavior of Holomorphic Functions of Several Complex Variables MN 11 written by Elias M. Stein and published by Princeton University Press. This book was released on 2015-03-08 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Download or read book Boundary Behavior of Holomorphic Functions written by Fausto Di Biase and published by Birkhauser. This book was released on 2006-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Download or read book Geometric Analysis and Function Spaces written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Download or read book Behavior of Holomorphic Functions at Generating Submanifolds of the Boundary written by Vivian Susan Klein and published by . This book was released on 1979 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary Behavior of Holomorphic Functions on Domains of Finite Type written by Hyungwoon Koo and published by . This book was released on 1993 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reviews in Complex Analysis 1980 86 written by and published by . This book was released on 1989 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Normal Families and Normal Functions written by Peter V. Dovbush and published by CRC Press. This book was released on 2024-02-27 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.

Download or read book Geometry of Holomorphic Mappings written by Sergey Pinchuk and published by Springer Nature. This book was released on 2023-10-16 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Download or read book Boundary Behaviour of Holomorphic Functions on Bounded Symmetric Domains written by A. Koranyi and published by . This book was released on 1975 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Complex Analysis of Several Variables written by Yum-Tong Siu and published by American Mathematical Soc.. This book was released on 1984 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a collection of papers from the Symposium on Several Complex Variables held April 12-15, 1983 in Madison, Wisconsin. This book contains a selection of the presented papers as well as some contributed papers.

Download or read book The Boundary Behavior of Holomorphic Functions written by Baili Min and published by . This book was released on 2011 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of several complex variables, the Fatou type problems, the Lindelöf principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindelöf principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in C2.

Download or read book American Doctoral Dissertations written by and published by . This book was released on 1981 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Extension of Functions Holomorphic in a Submanifold in General Position and C up to Boundary to Strictly Pseudo convex Domains written by Manuel Elgueta and published by . This book was released on 1975 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Boundary Behavior of Holomorphic Functions in the Unit Disk written by Sister Claude Marie Faust and published by . This book was released on 1961 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Representation and Boundary Behavior of Certain Classes of Holomorphic Functions in Several Variables written by Ryan Keddie Tully-Doyle and published by . This book was released on 2015 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concerns the investigation of function theoretic properties of certain classes of holomorphic functions in two or more variables by means of operator theoretic methods. Of primary concern will be the Schur class, the class of holomorphic functions from the complex polydisk into the complex unit disk, and the Pick class, the class of holomorphic functions from the complex poly-upperhalfplane into the complex upperhalfplane. In more than two variables, our results will concern certain large subclasses of these functions that satisfy an operator-theoretic condition analogous to a classical inequality of functions of one variable due to von Neumann [vN51]. These subclasses are typically referred to as the Schur-Agler subclass of the Schur functions (introduced in [Agl90]), and the Loewner subclass of the Pick functions (introduced in [AMY12b]. (In one or two variables, these subclasses coincide with the whole class.) These functions are amenable to investigation by means of an operator-theoretic construct called a Hilbert space model, introduced in [Agl90], which relates operator theoretic properties with function theoretic behavior. Hilbert space models are associated with and closely related to the notion of a transfer function realization from engineering and control theory [Hel87]. In Chapter 2, we describe a generalization of Hilbert space models for Schur functions on the bidisk that is well-suited to the investigation of boundary behavior of a function at a class of singular points for the function on the 2-torus. We prove that generalized models with certain regularity properties exist at these singularities. We then solve two function theoretic problems. First, we characterize the directional derivatives of a function in the Schur class at a singular point on the torus where a Caratheodory condition holds (following the generalization of the Julia-Carathedory theorem in [AMY12]. Second, we develop a representation theorem for functions in the two-variable Pick class analogous to the Nevanlinna representation theorem characterizing the Cauchy transforms of positive measures on the real line. In Chapter 3, we investigate more closely the structure of the generalized Hilbert space model. We characterize the directional derivatives in terms of a rational function depending on the structure of a positive contraction associated with a generalized model of a given Schur function. We describe classes of generalized models corresponding to different classes of singular points in the boundary for a Schur function in two variables. In Chapter 4, we generalize to several variables the Nevanlinna representation first investigated in Chapter 2. We show that for the Loewner class, there are representation formulae in terms of densely-defined self-adjoint operators on a Hilbert space that classify completely the Loewner class. We identify four types of such representations, and we obtain function-theoretic conditions that are necessary and sufficient for a given function to possess a representation of each of the four types.

Download or read book Boundary Behavior of Holomorphic Functions on Pseudoconvex Domains written by 康素珍 and published by . This book was released on 1986 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: