Conditions for sectoriality and compactness of the resolvent for a non-self-adjoint Sturm--Liouville operator with singular distributional potential

Abstract

The aim of this paper is to find necessary and sufficient conditions for sectoriality and compactness of the resolvent for Sturm--Liouville operators with complex-valued potentials of the class $q\in W_{2,loc}^{-1}(\mathbb{R}_+)$ in terms of its generalized antiderivatives $s\in L_{2,loc}(\mathbb{R}_+)$.