Potential Theory in the Complex Plane

Potential Theory in the Complex Plane
Author: Thomas Ransford
Publisher: Cambridge University Press
Total Pages: 246
Release: 1995-03-16
Genre: Mathematics
ISBN: 9780521466547

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.

Complex Analysis and Potential Theory

Complex Analysis and Potential Theory
Author: Andre Boivin
Publisher: American Mathematical Soc.
Total Pages: 347
Release: 2012
Genre: Mathematics
ISBN: 0821891731

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

Complex Potential Theory
Author: Paul M. Gauthier
Publisher: Springer Science & Business Media
Total Pages: 565
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401109346

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

The Cauchy Transform, Potential Theory and Conformal Mapping
Author: Steven R. Bell
Publisher: CRC Press
Total Pages: 221
Release: 2015-11-04
Genre: Mathematics
ISBN: 1498727212

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

Pluripotential Theory

Pluripotential Theory
Author: Maciej Klimek
Publisher:
Total Pages: 296
Release: 1991
Genre: Mathematics
ISBN:

Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two concepts provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. A substantial proportion of the work is devoted to classical properties of subharmonic and plurisubharmonic functions, which makes the pluripotential theory available for the first time to a wide audience of analysts.

Logarithmic Potentials with External Fields

Logarithmic Potentials with External Fields
Author: Edward B. Saff
Publisher: Springer Science & Business Media
Total Pages: 517
Release: 2013-11-11
Genre: Mathematics
ISBN: 3662033291

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.

Potential Theory - ICPT 94

Potential Theory - ICPT 94
Author: Josef Kral
Publisher: Walter de Gruyter
Total Pages: 513
Release: 2011-10-13
Genre: Mathematics
ISBN: 3110818574

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.

Applied Complex Variables

Applied Complex Variables
Author: John W. Dettman
Publisher: Courier Corporation
Total Pages: 514
Release: 2012-05-07
Genre: Mathematics
ISBN: 0486158284

Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Harmonic Function Theory

Harmonic Function Theory
Author: Sheldon Axler
Publisher: Springer Science & Business Media
Total Pages: 266
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475781377

This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

Approximation, Complex Analysis, and Potential Theory

Approximation, Complex Analysis, and Potential Theory
Author: Norair Arakelian
Publisher: Springer Science & Business Media
Total Pages: 275
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401009791

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.