On sesquilinear forms for lower semibounded (singular) Sturm–Liouville operators

Abstract

Any self-adjoint extension of a (singular) Sturm–Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm–Liouville operator by using generalized boundary values. We provide these forms in detail in all possible cases (explicitly, when both endpoints are limit circle, when one endpoint is limit circle, and when both endpoints are limit point).