Separately superharmonic functions in product networks

Victor Anandam. "Separately superharmonic functions in product networks." Annales Polonici Mathematici 113.3 (2015): 209-241. <http://eudml.org/doc/280851>.

@article{VictorAnandam2015,
abstract = {Let X×Y be the Cartesian product of two locally finite, connected networks that need not have reversible conductance. If X,Y represent random walks, it is known that if X×Y is recurrent, then X,Y are both recurrent. This fact is proved here by non-probabilistic methods, by using the properties of separately superharmonic functions. For this class of functions on the product network X×Y, the Dirichlet solution, balayage, minimum principle etc. are obtained. A unique integral representation is given for any function that belongs to a restricted subclass of positive separately superharmonic functions in X×Y.},
author = {Victor Anandam},
journal = {Annales Polonici Mathematici},
keywords = {cartesian product of networks; separately superharmonic functions; product potentials},
language = {eng},
number = {3},
pages = {209-241},
title = {Separately superharmonic functions in product networks},
url = {http://eudml.org/doc/280851},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Victor Anandam
TI - Separately superharmonic functions in product networks
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 3
SP - 209
EP - 241
AB - Let X×Y be the Cartesian product of two locally finite, connected networks that need not have reversible conductance. If X,Y represent random walks, it is known that if X×Y is recurrent, then X,Y are both recurrent. This fact is proved here by non-probabilistic methods, by using the properties of separately superharmonic functions. For this class of functions on the product network X×Y, the Dirichlet solution, balayage, minimum principle etc. are obtained. A unique integral representation is given for any function that belongs to a restricted subclass of positive separately superharmonic functions in X×Y.
LA - eng
KW - cartesian product of networks; separately superharmonic functions; product potentials
UR - http://eudml.org/doc/280851
ER -