On Topologies and Boundaries in Potential Theory
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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 constanti...
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 ¿ short survey.
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