Separately superharmonic functions in product networks

• Autorzy: Victor Anandam
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 31C20: Discrete potential theory and numerical methods
• 31C10: Pluriharmonic and plurisubharmonic functions
• 32U05: Plurisubharmonic functions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 113
• Numer: 3
• Strony: 209-241

Daty

wydano

2015

Twórcy

autor

Victor Anandam

• Institute of Mathematical Sciences, Chennai, Tamil Nadu, India 600 113

Identyfikatory

DOI

10.4064/ap113-3-1