Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions

Thomas Patrick Pawlaschyk. "Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions." Annales Polonici Mathematici 117.1 (2016): 17-39. <http://eudml.org/doc/286464>.

@article{ThomasPatrickPawlaschyk2016,
abstract = {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.},
author = {Thomas Patrick Pawlaschyk},
journal = {Annales Polonici Mathematici},
keywords = {q-plurisubharmonic; q-convex; convex; Shilov boundary; Bergman boundary},
language = {eng},
number = {1},
pages = {17-39},
title = {Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions},
url = {http://eudml.org/doc/286464},
volume = {117},
year = {2016},
}

TY - JOUR
AU - Thomas Patrick Pawlaschyk
TI - Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions
JO - Annales Polonici Mathematici
PY - 2016
VL - 117
IS - 1
SP - 17
EP - 39
AB - 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.
LA - eng
KW - q-plurisubharmonic; q-convex; convex; Shilov boundary; Bergman boundary
UR - http://eudml.org/doc/286464
ER -