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Author : Thomas Ransford
Publisher : Cambridge University Press
Page : 246 pages
File Size : 55,6 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 0521466547
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Author : Thomas Ransford,Dr Ransford Thomas
Publisher : Cambridge University Press
Page : 243 pages
File Size : 46,9 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362059
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Author : Tahir Aliyev Azero?lu,Promarz Melikovich Tamrazov
Publisher : World Scientific
Page : 301 pages
File Size : 44,8 Mb
Release : 2007
Category : Science
ISBN : 9789812705983
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.
Author : Oliver Dimon Kellogg
Publisher : Courier Corporation
Page : 404 pages
File Size : 48,8 Mb
Release : 1953-01-01
Category : Science
ISBN : 0486601447
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,5 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789814475716
Author : Paul M. Gauthier
Publisher : Springer Science & Business Media
Page : 565 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401109345
Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993
Author : Andre Boivin,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 49,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891735
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.
Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 50,5 Mb
Release : 2006-06-19
Category : Mathematics
ISBN : 9783540310624
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.
Author : Kalyan Kumar Roy
Publisher : Springer Science & Business Media
Page : 661 pages
File Size : 40,6 Mb
Release : 2007-11-15
Category : Science
ISBN : 9783540723349
This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.
Author : S. V. Rogosin
Publisher : Unknown
Page : 128 pages
File Size : 55,7 Mb
Release : 2014
Category : Electronic
ISBN : 1908106409
Author : Norair Arakelian,Paul M. Gauthier
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401009799
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.
Author : Dmitry Khavinson,Erik Lundberg
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 40,7 Mb
Release : 2018-07-09
Category : Differential equations, Linear
ISBN : 9781470437800
Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.
Author : G.M. Khenkin,A.G. Vitushkin
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642578823
Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functions in complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given.
Author : Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 44,6 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9783110818574
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.
Author : Edward B. Saff,Vilmos Totik
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 54,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662033296
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.