Choquet's theory and the Dirichlet problem
Copyright policy )Choquet's theory and the Dirichlet problem
The aim of the paper is to illustrate the importance of the notion of convex sets in potential theory and functional analysis. The authors start with a motivation from several different fields arriving at the question whether it is possible to find a measure in the theorem on integral representation which is concentrated only in the set of extremal points. G. Choquet solved the problem in the 1950s founding what is called Choquet's theory. The rest of the paper is devoted to various aspects of the theory in the more general context of function spaces.
- Charles University Czech Republic
- Charles University / Faculty of Mathematics and Physics Czech Republic
Mathematics(all), Integral representations, integral operators, integral equations methods in higher dimensions, Convex sets in topological linear spaces; Choquet theory, Choquet boundary, Choquet's theory, Harmonic, subharmonic, superharmonic functions in higher dimensions, Dirichlet boundary value problem, Martin boundary theory, maximum principle, harmonic function, geometry of convex sets, General convexity, Boundary value and inverse problems for harmonic functions in higher dimensions, representing measure, harmonic functions, Dirichlet problem
Mathematics(all), Integral representations, integral operators, integral equations methods in higher dimensions, Convex sets in topological linear spaces; Choquet theory, Choquet boundary, Choquet's theory, Harmonic, subharmonic, superharmonic functions in higher dimensions, Dirichlet boundary value problem, Martin boundary theory, maximum principle, harmonic function, geometry of convex sets, General convexity, Boundary value and inverse problems for harmonic functions in higher dimensions, representing measure, harmonic functions, Dirichlet problem
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