Regularization of singular Sturm–Liouville equations

Abstract. The paper deals with the singular Sturm-Liouville expressions l(y) = −(py′) ′ + qy with the coefficients q = Q′, 1/p,Q/p,Q2/p ∈ L1, where the derivative of the function Q is understood in the sense of distributions. Due to a new regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonical form. 1