It is proved if an irreducible, strong Feller symmetric Markov process possesses a tightness property, then its semi-group is an L2 -compact operator. In this paper, applying this fact, we prove probabilistically the compactness of Dirichlet-Laplacians and Schrödinger operators.
|Number of pages||16|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2017 Jan 1|
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