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.
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.
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>. .
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.
The Hilbert Transform Of Schwartz Distributions And Applications
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Author : J. N. Pandey
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
The Hilbert Transform Of Schwartz Distributions And Applications written by J. N. Pandey and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
This book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers. The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, high-energy physics, potentialtheory problems, and others. Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definition could alsoform the basis for a unified theory of the Hilbert transform ofperiodic, as well as nonperiodic, functions. The Hilbert transform and the approximate Hilbert transform ofperiodic functions are worked out in detail for the first time inbook form and can be used to solve Laplace's equation with periodicboundary conditions. Among the many theoretical results proved inthis book is a Paley-Wiener type theorem giving thecharacterization of functions and generalized functions whoseFourier transforms are supported in certain orthants of Rn. Placing a strong emphasis on easy application of theory andtechniques, the book generalizes the Hilbert problem in higherdimensions and solves it in function spaces as well as ingeneralized function spaces. It simplifies the one-dimensionaltransform of distributions; provides solutions to thedistributional Hilbert problems and singular integral equations;and covers the intrinsic definition of the testing function spacesand its topology. The book includes exercises and review material for all majortopics, and incorporates classical and distributional problems intothe main text. Thorough and accessible, it explores new ways to usethis important integral transform, and reinforces its value in bothmathematical research and applied science. The Hilbert transform made accessible with many new formulas anddefinitions Written by today's foremost expert on the Hilbert transform ofgeneralized functions, this combined text and reference covers theHilbert transform of distributions and the space of periodicdistributions. The author provides a consistently accessibletreatment of this advanced-level subject and teaches techniquesthat can be easily applied to theoretical and physical problemsencountered by mathematicians, applied scientists, and graduatestudents in mathematics and engineering. Introducing many new inversion formulas that have been developedand applied by the author and his research associates, the book: * Provides solutions to the distributional Hilbert problem andsingular integral equations * Focuses on the Hilbert transform of Schwartz distributions,giving intrinsic definitions of the space H(D) and its topology * Covers the Paley-Wiener theorem and provides many importanttheoretical results of importance to research mathematicians * Provides the characterization of functions and generalizedfunctions whose Fourier transforms are supported in certainorthants of Rn * Offers a new definition of the Hilbert transform of the periodicfunction that can be used for computational purposes in signalprocessing * Develops the theory of the Hilbert transform of periodicdistributions and the approximate Hilbert transform of periodicdistributions * Provides exercises at the end of each chapter--useful toprofessors in planning assignments, tests, and problems
Hilbert Transform In Fourier Spectroscopy
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Author : Hajime Sakai
language : en
Publisher:
Release Date : 1966
Hilbert Transform In Fourier Spectroscopy written by Hajime Sakai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Fourier analysis 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.