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Book
Potential Theory : Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Stresa (Varese), Italy, July 2-10, 1969
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ISBN: 3642110835 3642110843 Year: 2011 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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M. Brelot: Historical introduction.- H. Bauer: Harmonic spaces and associated Markov processes.- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel.- J. Deny: Méthodes hilbertiennes en theory du potentiel.- J.L. Doob: Martingale theory – Potential theory.- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés.


Book
Distribution of resonances in scattering by thin barriers
Author:
ISBN: 9781470435721 1470435721 Year: 2019 Publisher: Providence American Mathematical Society

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The author studies high energy resonances for the operators $-Delta_{partialOmega,delta}:=-Delta delta_{partialOmega}otimes Vquad extrm{and}quad -Delta_{partialOmega,delta'}:=-Delta delta_{partialOmega}'otimes Vpartial_u$ where $Omegasubset{mathbb{R}}^{d}$ is strictly convex with smooth boundary, $V:L^{2}(partialOmega)o L^{2}(partialOmega)$ may depend on frequency, and $delta_{partialOmega}$ is the surface measure on $partialOmega$.


Book
Multivariate polysplines : applications to numerical and wavelet analysis
Author:
ISBN: 1281023345 9786611023348 0080525008 Year: 2001 Publisher: San Diego, Calif. : Academic Press,

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Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions.Multivariate polysplines have applications in the design of surfaces and ""smoothing"" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effecti


Book
Growth Theory of Subharmonic Functions
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ISBN: 3764388854 3764388862 Year: 2009 Publisher: Basel : Birkhäuser Basel : Imprint: Birkhäuser,

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In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables. The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function. All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.


Book
A Course on Tug-of-War Games with Random Noise : Introduction and Basic Constructions
Author:
ISBN: 3030462099 3030462080 Year: 2020 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.


Book
Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics
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ISBN: 3030225909 3030225917 Year: 2019 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.


Book
Markov processes and potential theory
Authors: --- ---
ISBN: 1281766402 9786611766405 0080873413 0123745721 9780080873411 9780123745729 Year: 1968 Publisher: New York : Academic Press,

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Markov processes and potential theory

Probabilities and potential C : potential theory for discrete and continuous semigroups
Authors: --- --- ---
ISBN: 1281793183 9786611793180 008087262X 0444703861 9780444703866 9780080872629 Year: 1988 Publisher: Amsterdam ; New York : Elsevier,

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This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of cont

Potential Theory in Applied Geophysics
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ISBN: 1281137324 9786611137328 354072334X 3540720898 3642091253 Year: 2008 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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"Potential Theory in Applied Geophysics" 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. Behaviour of the scalar and vector potential and the nature of the solutions of these boundary value problems are shown along with the use of complex variables and conformal transformation, Green's theorem, Green's functions and its use in integral equation. Finite element and finite difference methods for two-dimensional potential problems are discussed in considerable detail. The analytical continuation of the potential field and inverse theory, used for the interpretation of potential field data, are also demonstrated.

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