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- MakaleAçık Erişim2025Scopus SJRQ3Direct and Inverse Scattering Problems for Sturm-Liouville Operator with Discontinuous Coefficient Under Discontinuity Conditions
Akcay, Ozge; Kosar, Nida Palamut
This paper deals with the study of the direct and inverse problems of scattering theory for Sturm-Liouville operator with piecewise continuous coefficient under the discontinuity conditions at the interior point of the positive semi-axis. The scattering properties are examined and the eigenfunction expansion is obtained. The fundamental equation or Marchenko-type equation of the inverse scattering problem is derived and an algorithm of the reconstruction of the potential according to scattering data of this problem is given. Moreover, the continuity of scattering function of this problem is examined.
- MakaleAçık Erişim2024Scopus SJRQ2THE SPECTRUM AND PRINCIPAL FUNCTIONS OF A NONSELF-ADJOINT STURM-LIOUVILLE OPERATOR WITH DISCONTINUITY CONDITIONS
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.
- MakaleAçık Erişim2024Scopus SJRQ4Investigation of the Spectrum of Nonself-Adjoint Discontinuous Sturm-Liouville Operator
Akçay, Özge; Koşar, Nida Palamut
In this paper, we study nonself-adjoint Sturm-Liouville operator containing both the discontinuous coefficient and discontinuity conditions at some point on the positive half-line. The eigenvalues and the spectral singularities of this problem are examined and it is proved that this problem has a finite number of spectral singularities and eigenvalues with finite multiplicities under two different additional conditions. Furthermore, the principal functions corresponding to the eigenvalues and the spectral singularities of this operator are determined.
- MakaleYalnız künye2022Scopus SJRQ3On the investigation of a discontinuous Sturm-Liouville operator of scattering theory
Akcay, Ozge
This paper deals with the investigation of the direct scattering problem for the Sturm-Liouville operator containing both the discontinuous coefficient and discontinuity conditions at some point on the positive half-line. The integral representation of the Jost solution is obtained and the properties of its kernel function are given. A total collection of the scattering data is constructed and the behavior of the scattering function at infinity is examined.
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