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Published online by Cambridge University Press: 20 November 2018
If the differential expression l(y) = — y” + g(x)y generates a closed operator L on L2(— ∞, ∞), with domain D consisting of those functions y ∈ L2 with absolutely continuous derivatives and such that l(y) ∈ L2. The case where g(x) is real-valued has been extensively investigated and yields an expansion of any ƒ ∈ L2 in terms of the characteristic functions of L. We shall investigate the case where g is complex-valued.