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On the Martin boundary of weakly coupled balayage spaces. (English) Zbl 1120.31005
In the framework of axiomatic potential theory as developed by J. Bliedtner and W. Hansen [Potential theory. An analytic and probabilistic approach to balayage. Universitext. Berlin etc.: Springer-Verlag (1986; Zbl 0706.31001)], a characterization for balayage spaces on countable topological spaces is proved. This is an extension of results obtained by M. Meyer [Potential theory, Proc. Conf., Prague/Czech. 1987, 237–246 (1988; Zbl 0691.31004)] and corresponds to results obtained by N. Bouleau [J. Math. Pures Appl. (9) 59, 187–240 (1980; Zbl 0403.60068)]. Large classes of examples fit into this setting.
Also, some results concerning the Choquet-type integral representation of positive harmonic functions for weakly coupled balayage spaces are presented.

31D05 Axiomatic potential theory
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
60J35 Transition functions, generators and resolvents
60J45 Probabilistic potential theory