Compactness of Schrödinger semigroups with unbounded below potentials |
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Authors: | Feng-Yu Wang Jiang-Lun Wu |
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Institution: | aSchool of Mathematical Sciences & Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China;bDepartment of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK |
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Abstract: | By using the super Poincaré inequality of a Markov generator L0 on L2(μ) over a σ-finite measure space (E,F,μ), the Schrödinger semigroup generated by L0−V for a class of (unbounded below) potentials V is proved to be L2(μ)-compact provided μ(V?N)<∞ for all N>0. This condition is sharp at least in the context of countable Markov chains, and considerably improves known ones on, e.g., Rd under the condition that V(x)→∞ as |x|→∞. Concrete examples are provided to illustrate the main result. |
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Keywords: | MSC: 47G30 60G51 |
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