On a Certain Semiclassical Problem on Wiener Spaces

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.