Abstract
It is proved if an irreducible, strong Feller symmetric Markov process possesses a tightness property, then its semi-group is an $L^2$-compact operator. In this paper, applying this fact, we prove probabilistically the compactness of Dirichlet-Laplacians and Schrödinger operators.
Citation
Masayoshi Takeda. Yoshihiro Tawara. Kaneharu Tsuchida. "Compactness of Markov and Schrödinger semi-groups: A probabilistic approach." Osaka J. Math. 54 (3) 517 - 532, July 2017.
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