Extremal properties of the first eigenvalue of Schrödinger-type operators

Abstract

Given a separable, locally compact Hausdorff space $X$ and a positive Radon measure $m(dx)$ on it, we study the problem of finding the potential $V(x)\ge 0$ that maximizes the first eigenvalue of the Schrödinger-type operator $L+V(x)$; $L$ is the generator of a local Dirichlet form $(a,D[a])$ on $L^2(X,m(dx))$.

15 pages. Accepted for publication on Journal of Functional Analysis