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. 365–392DOI 10.2977/PRIMS/1145476107