On topologies and boundaries in potential theory
著者
書誌事項
On topologies and boundaries in potential theory
（Lecture notes in mathematics, 175）
Springer-Verlag, 1971
- : Germany
- : U.S.
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注記
"Enlarged edition of a course of lectures delivered in 1966."
Bibliography: p. [165]-172
内容説明・目次
目次
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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