Homogeneous Rank One Perturbations and Inverse Square Potentials

Abstract

Following [2, 3, 5], I describe several exactly solvable families of closed operators on L²[0,∞]. Some of these families are defined by the theory of singular rank one perturbations. The remaining families are SchrÖdinger operators with inverse square potentials and various boundary conditions. I describe a close relationship between these families. In all of them one can observe interesting “renormalization group flows” (action of the group of dilations).