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The Cauchy Transform
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Book Synopsis The Cauchy Transform, Potential Theory and Conformal Mapping by : Steven R. Bell
Download or read book The Cauchy Transform, Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 2015-11-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Cauchy Transform by : Joseph A. Cima
Download or read book The Cauchy Transform written by Joseph A. Cima and published by American Mathematical Soc.. This book was released on 2006 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory by : Xavier Tolsa
Download or read book Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory written by Xavier Tolsa and published by Springer Science & Business Media. This book was released on 2013-12-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Real Variable Method for the Cauchy Transform, and Analytic Capacity by : Takafumi Murai
Download or read book A Real Variable Method for the Cauchy Transform, and Analytic Capacity written by Takafumi Murai and published by Springer. This book was released on 2006-11-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Cauchy Transform by : Joseph A. Cima
Download or read book The Cauchy Transform written by Joseph A. Cima and published by American Mathematical Society(RI). This book was released on 2014-05-21 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform by : Xavier Tolsa
Download or read book Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform written by Xavier Tolsa and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the proof of two related results. The first one asserts that if is a Radon measure in satisfyingfor -a.e. , then is rectifiable. Since the converse implication is already known to hold, this yields the following characterization of rectifiable sets: a set with finite -dimensional Hausdorff measure is rectifiable if and only ifH^1x2EThe second result of the monograph deals with the relationship between the above square function in the complex plane and the Cauchy transform . Assuming that has linear growth, it is proved that is bounded in if and only iffor every square .
Book Synopsis Vector-valued Laplace Transforms and Cauchy Problems by : Wolfgang Arendt
Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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>. .
Download or read book The Cauchy Transform, ... written by Bell and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Real Variable Method for the Cauchy Transform and Applications to Analytic Capacity by : Takafumi Murai
Download or read book A Real Variable Method for the Cauchy Transform and Applications to Analytic Capacity written by Takafumi Murai and published by . This book was released on 1987 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hilbert Transforms by : Frederick W. King
Download or read book Hilbert Transforms written by Frederick W. King and published by Encyclopedia of Mathematics an. This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.
Book Synopsis A Real Variable Method for the Cauchy Transform, and Analytic Capacity by :
Download or read book A Real Variable Method for the Cauchy Transform, and Analytic Capacity written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Radon Transform by : Sigurdur Helgason
Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 1999-08-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Book Synopsis Hilbert Transform in Fourier Spectroscopy by : Hajime Sakai
Download or read book Hilbert Transform in Fourier Spectroscopy written by Hajime Sakai and published by . This book was released on 1966 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical and Multilinear Harmonic Analysis by : Camil Muscalu
Download or read book Classical and Multilinear Harmonic Analysis written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Book Synopsis An Introduction to Laplace Transforms and Fourier Series by : P.P.G. Dyke
Download or read book An Introduction to Laplace Transforms and Fourier Series written by P.P.G. Dyke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Book Synopsis Hermitian Analysis by : John P. D'Angelo
Download or read book Hermitian Analysis written by John P. D'Angelo and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.
Book Synopsis Singular Integrals and Differentiability Properties of Functions (PMS-30), Volume 30 by : Elias M. Stein
Download or read book Singular Integrals and Differentiability Properties of Functions (PMS-30), Volume 30 written by Elias M. Stein and published by Princeton University Press. This book was released on 2016-06-02 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself. Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance. Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.
