On real continuous kernels satisfying the semi-complete maximum principle (Q1089127)

Taking notice of a potential theoretic property of the logarithmic kernel, we investigate a real continuous kernel V on a locally compact space satisfying the semi-complete maximum principle with respect to a certain positive Radon measure m. Under some assumptions, we construct the resolvent and the semi-group associated with V. We remark that they are uniformly recurrent and m is the (only) invariant measure of their transposed kernels.