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Transactions of the American Mathematical Society

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Compactness of symmetric Markov semigroups and boundedness of eigenfunctions


Author: Masayoshi Takeda
Journal: Trans. Amer. Math. Soc. 372 (2019), 3905-3920
MSC (2010): Primary 60J45; Secondary 60J75, 31C25, 31C05
DOI: https://doi.org/10.1090/tran/7664
Published electronically: February 22, 2019
MathSciNet review: 4009422
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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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Additional Information

Masayoshi Takeda
Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
Email: takeda@math.tohoku.ac.jp

DOI: https://doi.org/10.1090/tran/7664
Received by editor(s): October 29, 2017
Received by editor(s) in revised form: July 5, 2018
Published electronically: February 22, 2019
Additional Notes: The author was supported in part by Grant-in-Aid for Scientific Research (No.26247008(A)), Japan Society for the Promotion of Science.
Article copyright: © Copyright 2019 American Mathematical Society