Self-adjointness of Schroedinger operators with singular potentials

TL;DR

This paper investigates the self-adjointness of one-dimensional Schrödinger operators with singular distributional potentials, extending classical theorems to broader classes of potentials and clarifying their domain properties.

Contribution

It extends the Povzner-Wienholtz theorem to Schrödinger operators with distributional potentials in W^{-1}_{2,loc}(R), providing new insights into their self-adjointness and domain characteristics.

Findings

Extended self-adjointness criteria for singular potentials

Characterized domains of Schrödinger operators with distributional potentials

Provided conditions for self-adjointness in broader potential classes

Abstract

We study one-dimensional Schroedinger operators S with real-valued distributional potentials q in W^{-1}_{2,loc}(R) and prove an extension of the Povzner-Wienholtz theorem on self-adjointness of bounded below S thus providing additional information on its domain. The results are further specified for q in W^{-1}_{2,unif}(R).