On Topologies and Boundaries in Potential Theory
Brelot, Marcel.
On Topologies and Boundaries in Potential Theory Enlarged edition of a course of lectures delivered in 1966 / [electronic resource] : by Marcel Brelot. - VIII, 180 p. online resource. - Lecture Notes in Mathematics, 175 0075-8434 ; . - Lecture Notes in Mathematics, 175 .
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.
9783540364474
10.1007/BFb0060353 doi
Mathematics.
Mathematics, general.
QA1-939
510
On Topologies and Boundaries in Potential Theory Enlarged edition of a course of lectures delivered in 1966 / [electronic resource] : by Marcel Brelot. - VIII, 180 p. online resource. - Lecture Notes in Mathematics, 175 0075-8434 ; . - Lecture Notes in Mathematics, 175 .
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.
9783540364474
10.1007/BFb0060353 doi
Mathematics.
Mathematics, general.
QA1-939
510