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.

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.

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.

Potential Theory

Potential Theory
Author: Masanori Kishi
Publisher: Walter de Gruyter
Total Pages: 417
Release: 2011-05-02
Genre: Mathematics
ISBN: 3110859068

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.

Orthogonal Polynomials and Special Functions

Orthogonal Polynomials and Special Functions
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 2006-06-19
Genre: Mathematics
ISBN: 3540310622

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

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.