Kosar, N.P.; Akcay, O.

This paper deals with the nonself-adjoint Sturm-Liouville operator (or one-dimensional time-independent Schrödinger operator) with discontinuity conditions on the positive half line. In this study, the spectral singularities and the eigenvalues are investigated and it is proved that this problem has a finite number of spectral singularities and eigenvalues with finite multiplicities under two additional conditions. Moreover, we determine the principal functions with respect to the eigenvalues and the spectral singularities of this operator.

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