We investigate the existence and properties of the Jost solution associated with the differential equation −y + q(x)y = λy, x 0, for a class of real-or complex-valued slowly decaying potentials q. In particular, it is shown how the traditional condition q ∈ L(R + ) for the existence of the Jost solution can be replaced by q ∈ L(R + ) for a class of potentials considered here. We also examine the asymptotics of the Titchmarsh-Weyl function for a class of real-or complex-valued slowly decaying potentials and the form of the spectral density for a class of real-valued slowly decaying potentials.

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