Homogeneous Rank One Perturbations and Inverse Square Potentials

摘要

Following [2, 3, 5], I describe several exactly solvable families of closed operators on L~2[ 0 , ∞ [. Some of these families are defined by the theory of singular rank one perturbations. The remaining families are Schr?dinger 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) .