On a Certain Semiclassical Problem on Wiener Spaces

Shigeki Aida

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)365-392
Number of pages28
JournalPublications of the Research Institute for Mathematical Sciences
Volume39
Issue number2
DOIs
Publication statusPublished - 2003 Sep

ASJC Scopus subject areas

  • Mathematics(all)

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