A Real Variable Method For The Cauchy Transform And Analytic Capacity
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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.
A Real Variable Method For The Cauchy Transform And Analytic Capacity
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Author :
language : en
Publisher:
Release Date : 1988
A Real Variable Method For The Cauchy Transform And Analytic Capacity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Annotation. 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.
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.
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.
Analytic Capacity Rectifiability Menger Curvature And Cauchy Integral
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Author : Hervé M. Pajot
language : en
Publisher: Springer
Release Date : 2002-01-01
Analytic Capacity Rectifiability Menger Curvature And Cauchy Integral written by Hervé M. Pajot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.
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.
Selected Papers On Analysis Probability And Statistics
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Author : Katsumi Nomizu
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Selected Papers On Analysis Probability And Statistics written by Katsumi Nomizu 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 1994 with Mathematics categories.
This book presents papers in the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations, and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrödinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets, and the global structure of analytic functions.
Perspectives In Partial Differential Equations Harmonic Analysis And Applications
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Author : Dorina Mitrea
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Perspectives In Partial Differential Equations Harmonic Analysis And Applications written by Dorina Mitrea 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 2008 with Mathematics categories.
This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Icm 90 Satellite Conference Proceedings
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Author : Satoru Igari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Icm 90 Satellite Conference Proceedings written by Satoru Igari 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.
Proceedings of a Conference held in Sendai, Japan, August 14-18, 1990
Potential Theory Icpt 94
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Author : Josef Kral
language : en
Publisher: Walter de Gruyter
Release Date : 2011-10-13
Potential Theory Icpt 94 written by Josef Kral and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.