Integral representation for a class of multiply superharmonic functions

Gowrisankaran, Kohur. "Integral representation for a class of multiply superharmonic functions." Annales de l'institut Fourier 23.4 (1973): 105-143. <http://eudml.org/doc/74144>.

@article{Gowrisankaran1973,
abstract = {Let $\Omega _1,\ldots ,\Omega _n$ be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone $\{\bf C\}$ of the cone of positive $n$-superharmonic functions in $\Omega _1\times \ldots \times \Omega _n$ is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of $\{\bf C\}$. The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary and sufficient conditions for a positive $n$-superharmonic function to belong to $\{\bf C\}$ are given.},
author = {Gowrisankaran, Kohur},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {105-143},
publisher = {Association des Annales de l'Institut Fourier},
title = {Integral representation for a class of multiply superharmonic functions},
url = {http://eudml.org/doc/74144},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Gowrisankaran, Kohur
TI - Integral representation for a class of multiply superharmonic functions
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 4
SP - 105
EP - 143
AB - Let $\Omega _1,\ldots ,\Omega _n$ be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone ${\bf C}$ of the cone of positive $n$-superharmonic functions in $\Omega _1\times \ldots \times \Omega _n$ is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of ${\bf C}$. The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary and sufficient conditions for a positive $n$-superharmonic function to belong to ${\bf C}$ are given.
LA - eng
UR - http://eudml.org/doc/74144
ER -