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Author : Javier Tolsa Domènech
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (87 download)
Download or read book Curvature of measures, Cauchy singular integral and analytic capacity written by Javier Tolsa Domènech and published by . This book was released on 1998 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hervé M. Pajot
Publisher : Springer
ISBN 13 : 3540360743
Total Pages : 133 pages
Book Rating : 4.5/5 (43 download)
Download or read book Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral written by Hervé M. Pajot and published by Springer. This book was released on 2002-01-01 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Hervé Pajot
Publisher : Springer Science & Business Media
ISBN 13 : 9783540000013
Total Pages : 140 pages
Book Rating : 4.0/5 ( download)
Download or read book Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral written by Hervé Pajot and published by Springer Science & Business Media. This book was released on 2002-11-26 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Takafumi Murai
Publisher : Springer
ISBN 13 : 3540391053
Total Pages : 141 pages
Book Rating : 4.5/5 (43 download)
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.
Author : Xavier Tolsa
Publisher : Springer Science & Business Media
ISBN 13 : 3319005960
Total Pages : 402 pages
Book Rating : 4.3/5 (19 download)
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.
Author : Hasi Wulan
Publisher :
ISBN 13 : 9789514108020
Total Pages : 44 pages
Book Rating : 4.1/5 (8 download)
Download or read book Oscillation Theory of Higher Order Differential Equations in the Complex Plane written by Hasi Wulan and published by . This book was released on 1997 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William Beckner
Publisher : American Mathematical Soc.
ISBN 13 : 0821829033
Total Pages : 474 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis at Mount Holyoke written by William Beckner and published by American Mathematical Soc.. This book was released on 2003 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on harmonic analysis and related areas. The conference provided an opportunity for researchers and students to exchange ideas and report on progress in this large and central field of modern mathematics. The volume is suitable for graduate students and research mathematicians interested in harmonic analysis and related areas.
Author : Dorina Mitrea
Publisher : American Mathematical Soc.
ISBN 13 : 0821844245
Total Pages : 446 pages
Book Rating : 4.8/5 (218 download)
Download or read book Perspectives in Partial Differential Equations, Harmonic Analysis and Applications written by Dorina Mitrea and published by American Mathematical Soc.. This book was released on 2008 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Luca Capogna
Publisher : American Mathematical Soc.
ISBN 13 : 0821827456
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis and Boundary Value Problems written by Luca Capogna and published by American Mathematical Soc.. This book was released on 2001 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Author : David E. Edmunds
Publisher : Springer Science & Business Media
ISBN 13 : 940159922X
Total Pages : 655 pages
Book Rating : 4.4/5 (15 download)
Download or read book Bounded and Compact Integral Operators written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).
Author : Takafumi Murai
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Alexander Volberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821832522
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)
Download or read book Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces written by Alexander Volberg and published by American Mathematical Soc.. This book was released on 2003 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Pertti Mattila
Publisher : Cambridge University Press
ISBN 13 : 1009288083
Total Pages : 181 pages
Book Rating : 4.0/5 (92 download)
Download or read book Rectifiability written by Pertti Mattila and published by Cambridge University Press. This book was released on 2023-01-12 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad survey of the theory of rectifiability and its deep connections to numerous different areas of mathematics.
Author : American Mathematical Society
Publisher : American Mathematical Soc.
ISBN 13 : 082184881X
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)
Download or read book Selected Papers on Analysis and Differential Equations written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."
Author : James Dudziak
Publisher : Springer Science & Business Media
ISBN 13 : 1441967095
Total Pages : 338 pages
Book Rating : 4.4/5 (419 download)
Download or read book Vitushkin’s Conjecture for Removable Sets written by James Dudziak and published by Springer Science & Business Media. This book was released on 2011-02-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 1-5 of the book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.
Author : Francis Michael Christ
Publisher : American Mathematical Soc.
ISBN 13 : 0821807285
Total Pages : 144 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Singular Integral Operators written by Francis Michael Christ and published by American Mathematical Soc.. This book was released on 1991-01-07 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents an expanded account of lectures delivered at the NSF-CBMS Regional Conference on Singular Integral Operators, held at the University of Montana in the summer of 1989. The lectures are concerned principally with developments in the subject related to the Cauchy integral on Lipschitz curves and the T(1) theorem. The emphasis is on real-variable techniques, with a discussion of analytic capacity in one complex variable included as an application. The author has presented here a synthesized exposition of a body of results and techniques. Much of the book is introductory in character and intended to be accessible to the nonexpert, but a variety of readers should find the book useful.
Author : Albrecht Böttcher
Publisher : Birkhäuser
ISBN 13 : 3034889224
Total Pages : 408 pages
Book Rating : 4.0/5 (348 download)
Download or read book Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients. It includes an introduction to Carleson curves, Muckenhoupt weights, weighted norm inequalities, local principles, Wiener-Hopf factorization, and Banach algebras generated by idempotents. Some basic phenomena in the field and the techniques for treating them came to be understood only in recent years and are comprehensively presented here for the first time. The material has been polished in an effort to make advanced topics accessible to a broad readership. The book is addressed to a wide audience of students and mathematicians interested in real and complex analysis, functional analysis and operator theory.
