The Cauchy Transform
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The Cauchy Transform Potential Theory And Conformal Mapping
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Author : Steven R. Bell
language : en
Publisher: CRC Press
Release Date : 2015-11-04
The Cauchy Transform Potential Theory And Conformal Mapping written by Steven R. Bell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-04 with Mathematics categories.
The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f
The Cauchy Transform
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Author : Joseph A. Cima
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Cauchy Transform written by Joseph A. Cima 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 2006 with Mathematics categories.
The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.
Analytic Capacity The Cauchy Transform And Non Homogeneous Calder N Zygmund Theory
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Author : Xavier Tolsa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-16
Analytic Capacity The Cauchy Transform And Non Homogeneous Calder N Zygmund Theory written by Xavier Tolsa 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 2013-12-16 with Mathematics categories.
This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
A Real Variable Method For The Cauchy Transform And Analytic Capacity
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Author : Takafumi Murai
language : en
Publisher: Springer
Release Date : 2006-11-15
A Real Variable Method For The Cauchy Transform And Analytic Capacity written by Takafumi Murai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This research monograph studies the Cauchy transform on curves with the object of formulating a precise estimate of analytic capacity. The note is divided into three chapters. The first chapter is a review of the Calderón commutator. In the second chapter, a real variable method for the Cauchy transform is given using only the rising sun lemma. The final and principal chapter uses the method of the second chapter to compare analytic capacity with integral-geometric quantities. The prerequisites for reading this book are basic knowledge of singular integrals and function theory. It addresses specialists and graduate students in function theory and in fluid dynamics.
Vector Valued Laplace Transforms And Cauchy Problems
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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Vector Valued Laplace Transforms And Cauchy Problems written by Wolfgang Arendt 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 2013-11-11 with Mathematics categories.
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
The Cauchy Transform
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Author : Bell
language : en
Publisher:
Release Date : 1992
The Cauchy Transform written by Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
A Real Variable Method For The Cauchy Transform And Applications To Analytic Capacity
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Author : Takafumi Murai
language : en
Publisher:
Release Date : 1987
A Real Variable Method For The Cauchy Transform And Applications To Analytic Capacity written by Takafumi Murai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Analytic functions categories.
Integral Transforms And Their Applications
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Author : B. Davies
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Integral Transforms And Their Applications written by B. Davies 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 2013-11-27 with Mathematics categories.
This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems. It has its im mediate origin in lecture notes prepared for senior level courses at the Australian National University, although I owe a great deal to my colleague Barry Ninham, a matter to which I refer below. In preparing the notes for publication as a book, I have added a considerable amount of material ad- tional to the lecture notes, with the intention of making the book more useful, particularly to the graduate student - volved in the solution of mathematical problems in the physi cal, chemical, engineering and related sciences. Any book is necessarily a statement of the author's viewpoint, and involves a number of compromises. My prime consideration has been to produce a work whose scope is selective rather than encyclopedic; consequently there are many facets of the subject which have been omitted--in not a few cases after a preliminary draft was written--because I v believe that their inclusion would make the book too long.
Special Functions Their Applications
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Author : N. N. Lebedev
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Special Functions Their Applications written by N. N. Lebedev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions
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Author : Thomas Trogdon
language : en
Publisher: SIAM
Release Date : 2015-12-22
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions written by Thomas Trogdon and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Mathematics categories.
Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.?