Approximation Complex Analysis And Potential Theory

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Approximation, Complex Analysis, and Potential Theory

Author : Norair Arakelian
Publisher : Springer Science & Business Media
ISBN 13 : 9401009791
Total Pages : 275 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Approximation, Complex Analysis, and Potential Theory by : Norair Arakelian

Download or read book Approximation, Complex Analysis, and Potential Theory written by Norair Arakelian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Complex Analysis and Potential Theory

Author : Andre Boivin
Publisher : American Mathematical Soc.
ISBN 13 : 0821891731
Total Pages : 347 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Analysis and Potential Theory by : Andre Boivin

Download or read book Complex Analysis and Potential Theory written by Andre Boivin and published by American Mathematical Soc.. This book was released on 2012 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.

Complex Potential Theory

Author : Paul M. Gauthier
Publisher : Springer Science & Business Media
ISBN 13 : 9401109346
Total Pages : 565 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Complex Potential Theory by : Paul M. Gauthier

Download or read book Complex Potential Theory written by Paul M. Gauthier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993

The Cauchy Transform, Potential Theory and Conformal Mapping

Author : Steven R. Bell
Publisher : CRC Press
ISBN 13 : 9780849382703
Total Pages : 164 pages
Book Rating : 4.3/5 (827 download)

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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 1992-08-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods. The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.

Potential Theory in the Complex Plane

Author : Thomas Ransford
Publisher : Cambridge University Press
ISBN 13 : 9780521466547
Total Pages : 246 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Potential Theory in the Complex Plane by : Thomas Ransford

Download or read book Potential Theory in the Complex Plane written by Thomas Ransford and published by Cambridge University Press. This book was released on 1995-03-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.

Logarithmic Potentials with External Fields

Author : Edward B. Saff
Publisher : Springer Science & Business Media
ISBN 13 : 3662033291
Total Pages : 517 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Logarithmic Potentials with External Fields by : Edward B. Saff

Download or read book Logarithmic Potentials with External Fields written by Edward B. Saff and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.

Complex Analysis and Potential Theory

Author : Tahir Aliyev Azero?lu
Publisher : World Scientific
ISBN 13 : 9812705988
Total Pages : 301 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Complex Analysis and Potential Theory by : Tahir Aliyev Azero?lu

Download or read book Complex Analysis and Potential Theory written by Tahir Aliyev Azero?lu and published by World Scientific. This book was released on 2007 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from outstanding mathematicians, such as Samuel Krushkal, Reiner Khnau, Chung Chun Yang, Vladimir Miklyukov and others.It will help researchers to solve problems on complex analysis and potential theory and discuss various applications in engineering. The contributions also update the reader on recent developments in the field. Moreover, a special part of the volume is completely devoted to the formulation of some important open problems and interesting conjectures.

Approximation, Complex Analysis, and Potential Theory

Author : Norair Arakelian
Publisher : Springer
ISBN 13 : 9781402000287
Total Pages : 264 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Approximation, Complex Analysis, and Potential Theory by : Norair Arakelian

Download or read book Approximation, Complex Analysis, and Potential Theory written by Norair Arakelian and published by Springer. This book was released on 2001-09-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Complex Analysis and Potential Theory

Author :
Publisher :
ISBN 13 : 9814475718
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Complex Analysis and Potential Theory by :

Download or read book Complex Analysis and Potential Theory written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear and Complex Analysis Problem Book 3

Author : Victor P. Havin
Publisher : Springer
ISBN 13 : 3540483683
Total Pages : 529 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Linear and Complex Analysis Problem Book 3 by : Victor P. Havin

Download or read book Linear and Complex Analysis Problem Book 3 written by Victor P. Havin and published by Springer. This book was released on 2006-12-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!

Complex Analysis, Harmonic Analysis and Applications

Author : Robert Deville
Publisher : CRC Press
ISBN 13 : 9780582286986
Total Pages : 288 pages
Book Rating : 4.2/5 (869 download)

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Book Synopsis Complex Analysis, Harmonic Analysis and Applications by : Robert Deville

Download or read book Complex Analysis, Harmonic Analysis and Applications written by Robert Deville and published by CRC Press. This book was released on 1996-04-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariable complex analysis and harmonic analysis provide efficient techniques to study many applied mathematical problems. The main objective of a conference held in Bordeaux in June 1995, in honour of Professor Roger Gay, was to connect these mathematical fields with some of their applications. This was also the guideline for the fourteen contributions collected in this volume. Besides presenting new results, each speaker made a substantial effort in order to present an up to date survey of his field of research. All the subjects presented here are very active domains of research: integral geometry (with its relation to X-ray tomography), classical harmonic analysis and orthogonal polynomials, pluricomplex potential theory (with its deep connection with polynomial approximation), complex analytic methods in the theory of partial differentiable operators with constant coefficients (in the spirit of those initiated by Leon Ehrenpreis), Calderon-Zygmund operators and nonlinear operators, oscillatory integrals and resonance, and finally multivariable residue theory in its most recent developments. It is hoped that the reader will find enough insight in the different survey papers presented here to become involved with one of these subjects or to pursue further applications.

Classical Potential Theory

Author : David H. Armitage
Publisher : Springer Science & Business Media
ISBN 13 : 1447102339
Total Pages : 343 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Classical Potential Theory by : David H. Armitage

Download or read book Classical Potential Theory written by David H. Armitage and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.

Potential Theory in the Complex Plane

Author : Thomas Ransford
Publisher : Cambridge University Press
ISBN 13 : 9781107362055
Total Pages : 243 pages
Book Rating : 4.3/5 (62 download)

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Book Synopsis Potential Theory in the Complex Plane by : Thomas Ransford

Download or read book Potential Theory in the Complex Plane written by Thomas Ransford and published by Cambridge University Press. This book was released on 2014-05-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.

Potential Theory

Author : Josef Kral
Publisher : Springer Science & Business Media
ISBN 13 : 1461309816
Total Pages : 352 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Potential Theory by : Josef Kral

Download or read book Potential Theory written by Josef Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal with applications in physics and engineering, other concern potential theoretic aspects of function theory and complex analysis. Numerous papers are devoted to the theory of partial differential equations. Included are also many articles on axiomatic and abstract potential theory with its relations to probability theory. The present volume may thus be of intrest to mathematicians speciali zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.

Discrepancy of Signed Measures and Polynomial Approximation

Author : Vladimir V. Andrievskii
Publisher : Springer Science & Business Media
ISBN 13 : 1475749996
Total Pages : 444 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Discrepancy of Signed Measures and Polynomial Approximation by : Vladimir V. Andrievskii

Download or read book Discrepancy of Signed Measures and Polynomial Approximation written by Vladimir V. Andrievskii and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.

Function Spaces, Theory and Applications

Author : Ilia Binder
Publisher : Springer Nature
ISBN 13 : 3031392701
Total Pages : 487 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Function Spaces, Theory and Applications by : Ilia Binder

Download or read book Function Spaces, Theory and Applications written by Ilia Binder and published by Springer Nature. This book was released on 2024-01-12 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

Approximation Theory and Approximation Practice, Extended Edition

Author : Lloyd N. Trefethen
Publisher : SIAM
ISBN 13 : 1611975948
Total Pages : 375 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Approximation Theory and Approximation Practice, Extended Edition by : Lloyd N. Trefethen

Download or read book Approximation Theory and Approximation Practice, Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.