Hüseyin Tuna

Completeness of the rootvectors of a dissipative Sturm-Liouville operators on time scales

In this article, we consider dissipative Sturm-Liouville operators in the limit-circle case on time scales. Then, using the Livsics Theorem, we prove the completeness of the system of root vectors for dissipative Sturm-Liouville operators.

Dissipative q-Dirac operator with general boundary conditions

Abstract In this paper, we consider the symmetric q-Dirac operator. We describe dissipative, accumulative, self-adjoint and the other extensions of such operators with general boundary conditions. We construct a self-adjoint dilation of dissipative operator. Hence, we determine the scattering matrix of dilation. Later, we construct a functional model of this operator and define its characteristic function. Finally, we prove that all root vectors of this operator are complete.

On spectral properties of dissipative fourth order boundary-value problem with a spectral parameter in the boundary condition

In this article, we consider dissipative fourth order boundary-value problem in the Lim-4 case with the spectral parameter in the boundary condition. We use the maximal dissipative operator to construct a self-adjoint dilation of this operator and its incoming and outgoing spectral representations. Then, we determine the scattering matrix of dilation. We also construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding fourth order equation. Theorem on the completeness of the system of eigenvector and associated vectors of this operator are proved.

Limit-point criteria for q-Sturm-Liouville equations

Abstract In this article, the deficiency index problem of a singular q-Sturm-Liouville problem is studied. We establish some criteria under which the q-Sturm-Liouville equation is of limit-point case at infinity.

Spectral analysis of dissipative fractional Sturm–Liouville operators

Abstract We study fractional Sturm–Liouville operators. We give some basic definitions and properties of fractional calculus. Using the method of Pavlov [31, 30, 32], we prove a theorem on the completeness of the system of eigenvectors and associated vectors of dissipative fractional Sturm–Liouville operators.

Livšic’s theorem for q-Sturm—Liouville operators

In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livsic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.

Bir Boyutlu Dirac Operatörlerinin Özfonksiyonlar Sisteminin Tamlığı

Bu calismada Weyl limit cember durumunda kendine es olmayan bir boyutlu Dirac operatorleri calisilmistir. Krein teoremleri kullanilarak, bu operatorlerin oz ve asosye vektorler sisteminin tamligi arastirildi