On a Certain Semiclassical Problem on Wiener Spaces

Shigeki Aida

doi:10.2977/prims/1145476107

On a Certain Semiclassical Problem on Wiener Spaces

Shigeki Aida

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study asymptotic behavior of the spectrum of a Schrödinger type operator L_V^λ = L - λ²V on the Wiener space as λ → ∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.

Original language	English
Pages (from-to)	365-392
Number of pages	28
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	39
Issue number	2
DOIs	https://doi.org/10.2977/prims/1145476107
Publication status	Published - 2003 Sep

ASJC Scopus subject areas

Mathematics(all)

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AB - We study asymptotic behavior of the spectrum of a Schrödinger type operator LVλ = L - λ2V on the Wiener space as λ → ∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.

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On a Certain Semiclassical Problem on Wiener Spaces

Abstract

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