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 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 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 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 Boundary Behavior of Holomorphic Functions in the Unit Ball of C subscript N written by Paula A. Russo and published by . This book was released on 1984 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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:

Download or read book Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains written by David W. Catlin and published by . This book was released on 1978 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Holomorphic Functions of Several Variables written by R.C. Gunning and published by CRC Press. This book was released on 1990-05-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction 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.

Download or read book Introduction to Holomorphic Functions of Several Variables Volume I written by R.C. Gunning and published by Routledge. This book was released on 2018-05-02 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction 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.

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 Distributions and the Boundary Values of Analytic Functions written by E. J. Beltrami and published by Academic Press. This book was released on 2014-05-12 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.

Download or read book Introduction to Holomorphic Functions of Several Variables Volume II written by R.C. Gunning and published by Routledge. This book was released on 2018-05-02 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction 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.

Download or read book Bloch Besov Spaces and the Boundary Behavior of Their Functions written by Kyong Taik Hahn and published by . This book was released on 1993 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Some Consequences of the Boundary Behavior of the Caratheodory and Kobayashi Metrics and Applications to Normal Holomorphic Functions written by Gerardo Jose Aladro and published by . This book was released on 1985 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: