Abstract. Functions on infinite graphs are studied, keeping infinite electrical grids and Markov chains as models. The techniques used for this study are based on those from the classical and axiomatic potential theory and the analytic function theory on the complex plane and Riemann surfaces. This paper investigates Dirichlet problem in the context of an infinite network.

Received: May 2, 2011

AMS Subject Classification: 31C20, 31D05

Key Words and Phrases: Dirichlet problem on infinite subsets, condenser principle, balayage

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