Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 12
    On Dilation, Scattering and Spectral Theory for Two-Interval Singular Differential Operators
    (Soc Matematice Romania, 2015) Allahverdiev, Bilender P.; Uğurlu, Ekin; Ugurlu, Ekin; Matematik
    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.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    The Spectral Analysis of a System of First-Order Equations With Dissipative Boundary Conditions
    (Wiley, 2021) Ugurlu, Ekin
    This paper aims to share some completeness theorems related with a boundary value problem generated by a system of equations and non-self-adjoint (dissipative) boundary conditions. Indeed, we consider a system of equations that contains a continuous analogous of the orthogonal polynomials on the unit circle. Constructing the characteristic function of the related dissipative operator, we share some completeness theorems. Moreover, we give an explicit form of the self-adjoint dilation of the dissipative operator.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Direct Approach for the Characteristic Function of a Dissipative Operator With Distributional Potentials
    (Springer Basel Ag, 2020) Ugurlu, Ekin
    The main aim of this paper is to investigate the spectral properties of a singular dissipative differential operator with the help of its Cayley transform. It is shown that the Cayley transform of the dissipative differential operator is a completely non-unitary contraction with finite defect indices belonging to the class C-0. Using its characteristic function and the spectral properties of the resolvent operator, the complete spectral analysis of the dissipative differential operator is obtained. Embedding the Cayley transform to its natural unitary colligation, a Caratheodory function is obtained. Moreover, the truncated CMV matrix is established which is unitary equivalent to the Cayley transform of the dissipative differential operator. Furthermore, it is proved that the imaginary part of the inverse operator of the dissipative differential operator is a rank-one operator and the model operator of the associated dissipative integral operator is constructed as a semi-infinite triangular matrix. Using the characteristic function of the dissipative integral operator with rank-one imaginary component, associated Weyl functions are established.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Spectral Analysis of the Direct Sum Hamiltonian Operators
    (Natl inquiry Services Centre Pty Ltd, 2016) Ugurlu, Ekin; Allahverdiev, Bilender P.
    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.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    The Spectral Analysis of a Nuclear Resolvent Operator Associated With a Second Order Dissipative Differential Operator
    (Springer Heidelberg, 2017) Bairamov, Elgiz; Ugurlu, Ekin
    In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show that the inverse operator is a non-selfadjoint trace class operator. Using Lidskii's theorem, we introduce a complete spectral analysis of the second order dissipative differential operator. Moreover, we give a trace formula for the trace class integral operator.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    A New Method for Dissipative Dynamic Operator With Transmission Conditions
    (Springer Basel Ag, 2018) Ugurlu, Ekin; Tas, Kenan
    In this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.