Approximation, Complex Analysis, and Potential Theory

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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

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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

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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

Approximation Theory and Approximation Practice, Extended Edition

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Publisher : SIAM
ISBN 13 : 1611975948
Total Pages : 377 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 377 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 field’s 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.

Logarithmic Potentials with External Fields

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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

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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 Khnau, 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.

Complex Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 1441972889
Total Pages : 332 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Complex Analysis by : Joseph Bak

Download or read book Complex Analysis written by Joseph Bak and published by Springer Science & Business Media. This book was released on 2010-08-02 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

Complex Analysis And Potential Theory - Proceedings Of The Conference Satellite To Icm 2006

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Publisher : World Scientific
ISBN 13 : 9814475718
Total Pages : 301 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Complex Analysis And Potential Theory - Proceedings Of The Conference Satellite To Icm 2006 by : T Aliyev Azeroglu

Download or read book Complex Analysis And Potential Theory - Proceedings Of The Conference Satellite To Icm 2006 written by T Aliyev Azeroglu and published by World Scientific. This book was released on 2007-08-13 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 Kühnau, 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.

Complex Analysis

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Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Complex Analysis by : Elias M. Stein

Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Function Spaces, Theory and Applications

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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.

Advancements in Complex Analysis

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Publisher : Springer Nature
ISBN 13 : 3030401200
Total Pages : 538 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Advancements in Complex Analysis by : Daniel Breaz

Download or read book Advancements in Complex Analysis written by Daniel Breaz and published by Springer Nature. This book was released on 2020-05-12 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.

New Trends in Approximation Theory

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Publisher : Springer
ISBN 13 : 1493975439
Total Pages : 277 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis New Trends in Approximation Theory by : Javad Mashreghi

Download or read book New Trends in Approximation Theory written by Javad Mashreghi and published by Springer. This book was released on 2018-03-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

Introduction To The Theory Of Weighted Polynomial Approximation

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Publisher : World Scientific
ISBN 13 : 9814518050
Total Pages : 398 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Introduction To The Theory Of Weighted Polynomial Approximation by : H N Mhaskar

Download or read book Introduction To The Theory Of Weighted Polynomial Approximation written by H N Mhaskar and published by World Scientific. This book was released on 1997-01-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Discrepancy of Signed Measures and Polynomial Approximation

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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.

Potential Theory on Infinite Networks

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Publisher : Springer
ISBN 13 : 3540487980
Total Pages : 199 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Potential Theory on Infinite Networks by : Paolo M. Soardi

Download or read book Potential Theory on Infinite Networks written by Paolo M. Soardi and published by Springer. This book was released on 2006-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Potential Theory - ICPT 94

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Publisher : Walter de Gruyter
ISBN 13 : 3110818574
Total Pages : 513 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Potential Theory - ICPT 94 by : Josef Kral

Download or read book Potential Theory - ICPT 94 written by Josef Kral and published by Walter de Gruyter. This book was released on 2011-10-13 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Aspects of Contemporary Complex Analysis

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Publisher :
ISBN 13 :
Total Pages : 600 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Aspects of Contemporary Complex Analysis by : London Mathematical Society

Download or read book Aspects of Contemporary Complex Analysis written by London Mathematical Society and published by . This book was released on 1980 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: