JournalsprimsVol. 39, No. 2pp. 365–392

On a Certain Semiclassical Problem on Wiener Spaces

  • Shigeki Aida

    Osaka University, Japan
On a Certain Semiclassical Problem on Wiener Spaces cover
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Abstract

We study asymptotic behavior of the spectrum of a Schrödinger type operator LV_λ = L − λ2_V 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.

Cite this article

Shigeki Aida, On a Certain Semiclassical Problem on Wiener Spaces. Publ. Res. Inst. Math. Sci. 39 (2003), no. 2, pp. 365–392

DOI 10.2977/PRIMS/1145476107