Koşar, Nida Palamut; Koşar, Cem; Akcay, Ozge

In the present work, we investigate a (Formula presented.) -Dirac problem on the whole-line. Our primary objectives are threefold: to demonstrate the existence of a spectral function, to deduce the associated Parseval identity, and to formulate an eigenfunction expansion theorem that characterizes the behavior of the problem under consideration.

İncele

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.

İncele

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.

İncele

Akcay, O.

We deal with the inverse spectral problem of the discontinuous Sturm — Liouville operator. The aim is we to determine the potential q(x) and the boundary constant ℎ by a given spectral data. We provide the algorithm for reconstructing the potential q(x) from the spectral data.

İncele

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.

İncele

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.

AtıfScopus2

İncele

Akcay, Ozge

Bu çalışmada, pozitif yarı eksen üzerindeki bir noktada süreksizlik koşuluna sahip Sturm-Liouville operatörünün ters saçılma problemi ele alınmıştır. Ele alınan sınır değer probleminin saçılma verileri incelenmiştir. Rezolvent operatörü inşa edilmiş ve sınır değer probleminin özfonksiyonlarına göre ayrışım formülü elde edilmiştir. Ters saçılma probleminin temel denklemi veya modifiye edilmiş Marchenko denklemi elde edilmiş ve sınır değer probleminin saçılma verilerine göre potansiyel fonksiyonun inşa edilme algoritması verilmiştir.

AtıfOpenAlex1

İncele