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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 monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.
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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 --- Polyharmonic functions --- Spline theory --- Numerical solutions
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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 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.
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 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.
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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Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.
Mathematics --- Physical Sciences & Mathematics --- Geometry --- Mathematics. --- Algebraic geometry. --- Potential theory (Mathematics). --- Functions of complex variables. --- Geometry. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Potential Theory. --- Monge-Ampère equations --- Pluripotential theory --- Nonlinear theories --- Potential theory (Mathematics) --- Equations, Monge-Ampère --- Differential equations, Partial --- Geometry, algebraic. --- Differential equations, partial. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Partial differential equations --- Algebraic geometry --- Euclid's Elements --- Complex variables --- Elliptic functions --- Functions of real variables
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