On Topologies and Boundaries in Potential Theory. 1st ed. 1971

種類:

電子ブック

責任表示:

by Marcel Brelot

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1971

著者名:

• Brelot, Marcel.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 175

ISBN:

9783540364474 [3540364471]    

注記:

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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