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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • Masayoshi Takeda
  • Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
  • MR Author ID: 211690
  • Email: takeda@math.tohoku.ac.jp
  • 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.
  • © Copyright 2019 American Mathematical Society
  • 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
  • MathSciNet review: 4009422