Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions

• Autorzy: Thomas Patrick Pawlaschyk
• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of the Shilov boundary for some subfamilies of upper semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of that subclass attain their maximum. For certain subfamilies with simple structure we show the existence and uniqueness of the Shilov boundary. We provide its relation to the set of peak points and establish Bishop-type theorems. As an application we obtain a generalization of Bychkov's theorem which gives a geometric characterization of the Shilov boundary for q-plurisubharmonic functions on convex bounded domains.

Kategorie tematyczne

• 32F10: q -convexity, q -concavity
• 32U05: Plurisubharmonic functions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 117
• Numer: 1
• Strony: 17-39

Daty

wydano

2016

Twórcy

autor

Thomas Patrick Pawlaschyk

• Faculty of Mathematics and Natural Sciences, University of Wuppertal, 42119 Wuppertal, Germany

Identyfikatory

DOI

10.4064/ap3695-1-2016