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

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

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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Veröffentlicht in:Journal of theoretical probability 2018-06, Vol.31 (2), p.741-756
1. Verfasser: Takeda, Masayoshi
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Maximum principle
Operators
Probability Theory and Stochastic Processes
Statistics
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Beschreibung
Zusammenfassung: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-016-0734-0