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The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators

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Abstract

We give a necessary and sufficient condition for the maximum principle of Schrödinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schrödinger operators.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan

    Masayoshi Takeda

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  1. Masayoshi Takeda
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Correspondence to Masayoshi Takeda.

Additional information

The author was supported in part by Grant-in-Aid for Scientific Research No. 26247008(A) and Grant-in-Aid for Challenging Exploratory Research No. 25610018, Japan Society for the Promotion of Science.

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Takeda, M. The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators. J Theor Probab 31, 741–756 (2018). https://doi.org/10.1007/s10959-016-0734-0

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  • DOI: https://doi.org/10.1007/s10959-016-0734-0

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