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

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 $s\in L_{2,loc}({\mathbb{R}}_{+})$.