Departmental Bulletin Paper COMPACTNESS OF MARKOV AND SCHRÖ DINGER SEMI-GROUPS : A PROBABILISTIC APPROACH

Tawara, Yoshihiro  ,  Takeda, Masayoshi  ,  Tsuchida, Kaneharu

54 ( 3 )  , pp.517 - 532 , 2017-07 , Osaka University and Osaka City University, Departments of Mathematics
ISSN:00306126
NCID:AA00765910
Description
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.
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