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AuthorBrelot, Marcel. author
TitleOn Topologies and Boundaries in Potential Theory [electronic resource] : Enlarged edition of a course of lectures delivered in 1966 / by Marcel Brelot
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1971
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Descript VIII, 180 p. online resource


General notions of thinness and fine topology -- Notion of reduced function. Applications. Strong thinness and strong unthinness -- General results on fine limits -- Quasi-topological notions -- Weak thinness -- Notions in classical potential theory -- Classical fine topology-general properties -- Applications to balayage, weights and capacities -- Further study of classical thinness. Some applications -- Relations with the Choquet boundary -- Extension to axiomatic theories of harmonic functions -- Abstract minimal thinness, minimal boundary, minimal fine topology -- General compactification of constantinescu-cornea first examples of application -- Classical martin space the martin integral representation -- Classical martin space and minimal thinness -- Classical martin boundary dirichlet problem and boundary behaviour -- Comparison of both thinnesses. Fine limits and non-tangential limits. (Classical case. Examples) -- Martin space and minimal thinness in axiomatic theories โ{128}{148} short survey

Mathematics Mathematics Mathematics general


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