A Singular Boundary Value Problem for a Non-Self-Adjoint Differential Operator

Abstract

If the differential expression l(y) = — y” + g(x)y generates a closed operator L on L 2(— ∞, ∞), with domain D consisting of those functions y ∈ L 2 with absolutely continuous derivatives and such that l(y) ∈ L 2. The case where g(x) is real-valued has been extensively investigated and yields an expansion of any ƒ ∈ L 2 in terms of the characteristic functions of L. We shall investigate the case where g is complex-valued.