Compactness of symmetric Markov semigroups and boundedness of eigenfunctions

Takeda, Masayoshi

doi:10.1090/tran/7664

Compactness of symmetric Markov semigroups and boundedness of eigenfunctions
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by Masayoshi Takeda PDF

Trans. Amer. Math. Soc. 372 (2019), 3905-3920 Request permission

Abstract:

Let $X$ be an irreducible $m$-symmetric Markov process on $E$ with strong Feller property. In addition, suppose $X$ has a tightness property. We then show that the semigroup of $X$ is a compact operator on $L^2(E;m)$ and every eigenfunction has a bounded continuous version.

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