Marcel Brelot

On Topologies and Boundaries in Potential Theory

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Lecture Notes in Mathematics 175
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-05327-9
• 1971.
• Seitenzahl: 184
• Erscheinungstermin: 1. Januar 1971
• Englisch
• Abmessung: 235mm x 155mm x 11mm
• Gewicht: 314g
• ISBN-13: 9783540053279
• ISBN-10: 3540053271
• Artikelnr.: 23380250

Inhaltsangabe

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.