Browsing by Author "Allahverdiev, Bilender P."

Now showing 1 - 3 of 3

On dilation, scattering and spectral theory for two-interval singular differential operators
(Soc Matematice Romania, 2015) Uğurlu, Ekin; Uğurlu, Ekin; 238990
This paper aims to construct a space of boundary values for minimal symmetric singular impulsive-like Sturm-Liouville (SL) operator in limit-circle case at singular end points a, b and regular inner point c. For this purpose all maximal dissipative, accumulative and self-adjoint extensions of the symmetric operator are described in terms of boundary conditions. We construct a self-adjoint dilation of maximal dissipative operator, a functional model and we determine its characteristic function in terms of the scattering matrix of the dilation. The theorem verifying the completeness of the eigenfunctions and the associated functions of the dissipative SL operator is proved.
Scattering and spectral problems of the direct sum sturm-liouville operators
(Ministry Communications & High Technologies Republic Azerbaijan, 2017) Uğurlu, Ekin; Uğurlu, Ekin; 238990
In this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.
Spectral analysis of the direct sum hamiltonian operators
(Natl inquiry Services Centre Pty Ltd, 2016) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; 238990
In this paper we investigate the deficiency indices theory and the selfad-joint and nonselfadjoint (dissipative, accumulative) extensions of the minimal symmetric direct sum Hamiltonian operators. In particular using the equivalence of the Lax-Phillips scattering matrix and the Sz.-Nagy-Foias characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces.