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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.
Potential theory (Mathematics)  Mathematical analysis  517.1 Mathematical analysis  Mathematics.  Potential theory (Mathematics).  Potential Theory.  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mechanics
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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 $partialOmega$.
Potential theory (Mathematics)  Differentiable dynamical systems.  Potentiel, Théorie du.  Systèmes dynamiques.  Mathematical physics.  Mathematical physics  Physical mathematics  Physics  Mathematics
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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
Spline theory.  Polyharmonic functions.  Differential equations, Elliptic  Numerical solutions.  Functions, Polyharmonic  Harmonic functions  Potential theory (Mathematics)  Spline functions  Approximation theory  Interpolation
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Mathematical potential theory  517.57  Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Harmonic functions.  Potential theory (Mathematics)  Potential theory (Mathematics).  517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions  Harmonic functions  Fonctions harmoniques  Potentiel, Théorie du
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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.
Electronic books.  local.  Potential theory (Mathematics).  Subharmonic functions.  Subharmonic functions  Operations Research  Civil & Environmental Engineering  Engineering & Applied Sciences  Potential theory (Mathematics)  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Functions, Subharmonic  Mathematics.  Potential Theory.  Mathematical analysis  Mechanics  Functions of real variables
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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 tugofwar games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is selfcontained with many exercises, making the book suitable as a textbook for a graduate course, as well as for selfstudy. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.
Potential theory (Mathematics)  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Potential theory (Mathematics).  Probabilities.  Mathematical analysis.  Analysis (Mathematics).  Potential Theory.  Probability Theory and Stochastic Processes.  Analysis.  517.1 Mathematical analysis  Probability  Statistical inference  Combinations  Mathematics  Chance  Least squares  Mathematical statistics  Risk
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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.
Geometric function theory.  Functions of complex variables.  Potential theory (Mathematics).  Functions of a Complex Variable.  Potential Theory.  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Complex variables  Elliptic functions  Functions of real variables
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Markov processes and potential theory
Markov processes.  Potential theory (Mathematics)  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Analysis, Markov  Chains, Markov  Markoff processes  Markov analysis  Markov chains  Markov models  Models, Markov  Processes, Markov  Stochastic processes
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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
Probabilities.  Potential theory (Mathematics)  Semigroups.  Group theory  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Probability  Statistical inference  Combinations  Mathematics  Chance  Least squares  Mathematical statistics  Risk
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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 twodimensional 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.
Geophysics.  Potential theory (Mathematics)  Geological physics  Terrestrial physics  Earth sciences  Physics  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Physical geography.  Potential theory (Mathematics).  Geography.  Mathematics.  Geophysics/Geodesy.  Theoretical, Mathematical and Computational Physics.  Potential Theory.  Earth Sciences, general.  Applications of Mathematics.  Math  Science  Geography  Cosmography  World history  Mathematical physics.  Earth sciences.  Applied mathematics.  Engineering mathematics.  Engineering  Engineering analysis  Geosciences  Environmental sciences  Physical sciences  Physical mathematics  Mathematics
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