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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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Dynamics --- Potential theory (Mathematics) --- Strains and stresses --- Hydrodynamics --- Dynamique --- Potentiel, Théorie du --- Contraintes (Mécanique) --- Hydrodynamique --- Dynamics.
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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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"Fix d [greater than or equal to] 2, and s [epsilon] (d - 1, d). We characterize the non-negative locally finite non-atomic Borel measures [mu] in Rd for which the associated s-Riesz transform is bounded in L²([mu]) in terms of the Wolff energy. This extends the range of s in which the Mateu-Prat-Verdera characterization of measures with bounded s-Riesz transform is known. As an application, we give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator (-[delta])[infinity]/2, [infinity] [epsilon] (1, 2), in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions"--
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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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Function spaces --- Potential theory (Mathematics) --- Espaces fonctionnels --- Functionele ruimten --- Potentiaaltheorie --- Potentiel [Théorie du ] --- Function spaces. --- Potential theory (Mathematics). --- Potentiel, Théorie du --- Banach spaces. --- Banach, Espaces de. --- Espaces fonctionnels. --- Analyse fonctionnelle --- Functional analysis --- Functional analysis. --- Banach, Espaces de --- Theorie du potentiel
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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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Artificial intelligence. Robotics. Simulation. Graphics --- Electronics and optics of solids --- Crystals --- Potential theory (Mathematics) --- Crystallography --- Digital computer simulation --- Cristaux --- Potentiel, Théorie du --- Cristallographie --- Defects --- Congresses --- Data processing --- Défauts --- Congrès --- Informatique --- Potentiel, Théorie du --- Défauts --- Congrès --- Congresses.
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Mathematical potential theory --- Potential theory (Mathematics) --- Differential equations, Elliptic --- Calculus of variations --- Potentiel, Théorie du --- Equations différentielles elliptiques --- Calcul des variations --- Potentiel, Théorie du --- Equations différentielles elliptiques