Extremal Properties of the First Eigenvalueof Schrِdinger-Type Operators

Given a separable, locally compact Hausdorff spaceXand a positive Radon measurem(dx) on it, we study the problem of finding the potentialV(x)⩾0 that maximizes the first eigenvalue of the Schrödinger-type operatorL+V(x);Lis the generator of a local Dirichlet form (a, D[a]) onL2(X, m(dx)).