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Separately superharmonic functions in product networks

100%

Anandam V.

Annales Polonici Mathematici

2015

tom 113

nr 3

209-241

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.

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On a generalized logarithmic kernel and its potentials

45%

Anandam V., Brelot M.

Annales Polonici Mathematici

1981

tom 39

nr 1

15-29

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2 Annales Polonici Mathematici

2 Anandam V.

1 Brelot M.

1 2015

1 1981

Wyniki wyszukiwania

Separately superharmonic functions in product networks

On a generalized logarithmic kernel and its potentials