New Constructions Of Functions Holomorphic In The Unit Ball Of Cn
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New Constructions Of Functions Holomorphic In The Unit Ball Of Cn
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Author : Walter Rudin
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
New Constructions Of Functions Holomorphic In The Unit Ball Of Cn written by Walter Rudin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
New Constructions Of Functions Holomorphic In The Unit Ball Of C N
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Author : Walter Rudin
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
New Constructions Of Functions Holomorphic In The Unit Ball Of C N written by Walter Rudin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Uses as a starting point A B Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C DEGREESn$. This title simplifies the construction of such functions by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of pr
Spaces Of Holomorphic Functions In The Unit Ball
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Author : Kehe Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-22
Spaces Of Holomorphic Functions In The Unit Ball written by Kehe Zhu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-22 with Mathematics categories.
Can be used as a graduate text Contains many exercises Contains new results
Invariant Potential Theory In The Unit Ball Of Cn
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Author : Manfred Stoll
language : en
Publisher: Cambridge University Press
Release Date : 1994-05-12
Invariant Potential Theory In The Unit Ball Of Cn written by Manfred Stoll and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-12 with Mathematics categories.
This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.
The Mutually Beneficial Relationship Of Graphs And Matrices
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-06
The Mutually Beneficial Relationship Of Graphs And Matrices written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.
Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.
Malliavin Calculus And Its Applications
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Author : David Nualart
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Malliavin Calculus And Its Applications written by David Nualart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.
Calderon Zygmund Capacities And Operators On Nonhomogeneous Spaces
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Author : Alexander Volberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Calderon Zygmund Capacities And Operators On Nonhomogeneous Spaces written by Alexander Volberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Singular integral operators play a central role in modern harmonic analysis. Simplest examples of singular kernels are given by Calderon-Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderon-Zygmund operators. In the 1980's and early 1990's, Coifman, Weiss, and Christ noticed that the theory of Calderon-Zygmund operators can be generalized from Euclidean spaces to spaces of homogeneous type. The purpose of this book is to make the reader believe that homogeneity (previously considered as a cornerstone of the theory) is not needed. This claim is illustrated by presenting two harmonic analysis problems famous for their difficulty. The first problem treats semiadditivity of analytic and Lipschitz harmonic capacities. The volume presents the first self-contained and unified proof of the semiadditivity of these capacities. The book details Tolsa's solution of Painleve's and Vitushkin's problems and explains why these are problems of the theory of Calderon-Zygmund operators on nonhomogeneous spaces. The exposition is not dimension-specific, which allows the author to treat Lipschitz harmonic capacity and analytic capacity at the same time. The second problem considered in the volume is a two-weight estimate for the Hilbert transform. This problem recently found important applications in operator theory, where it is intimately related to spectral theory of small perturbations of unitary operators. The book presents a technique that can be helpful in overcoming rather bad degeneracies (i.e., exponential growth or decay) of underlying measure (volume) on the space where the singular integral operator is considered. These situations occur, for example, in boundary value problems for elliptic PDE's in domains with extremely singular boundaries. Another example involves harmonic analysis on the boundaries of pseudoconvex domains that goes beyond the scope of Carnot-Caratheodory spaces. The book is suitable for graduate students and research mathematicians interested in harmonic analysis.
Canadian Mathematical Bulletin
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Author :
language : en
Publisher:
Release Date : 1993-03
Canadian Mathematical Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03 with categories.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
Function Theory In The Unit Ball Of Cn
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Author : W. Rudin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Function Theory In The Unit Ball Of Cn written by W. Rudin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.