Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article The Characteristic Matrix Function of a Dissipative Hamiltonian Operator(Wiley, 2021) Ugurlu, EkinIn this paper, we consider a singular dissipative even-order Hamiltonian operator with a finite number of transmission conditions. Using coordinate-free approach, we construct the characteristic matrix-function of the Cayley transform of the dissipative operator. Using the equivalence of completeness property of root functions of Cayley transform and dissipative operator, we prove some completeness theorems. Moreover, we construct an explicit form of the resolvent operator of dissipative operator.Article Citation - WoS: 1Citation - Scopus: 1Direct Approach for the Characteristic Function of a Dissipative Operator With Distributional Potentials(Springer Basel Ag, 2020) Ugurlu, EkinThe 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: 2Citation - Scopus: 2Singular Dissipative Third-Order Operator and Its Characteristic Function(Springer Basel Ag, 2020) Ugurlu, EkinIn this work, we describe well-defined dissipative boundary conditions related with a singular third-order differential equation in lim-3 case at singular point. Using the characteristic function of the corresponding dissipative operator we introduce a completeness theorem.Article Citation - WoS: 1Citation - Scopus: 1Coordinate-Free Approach for the Characteristic Function of a Fourth-Order Dissipative Operator(Taylor & Francis inc, 2019) Ugurlu, EkinIn this article, we investigate some spectral properties of a singular dissipative fourth-order dissipative operator in case at the singular point. For this purpose we construct the characteristic function of both maximal simple dissipative operator and completely non-unitary contraction which is the Cayley transform of the dissipative operator. Using the properties of the characteristic operator-function we obtain the related results of the boundary value problem. Moreover we obtain the selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing eigenfunctions by using coordinate-free approach.Article Citation - WoS: 4Citation - Scopus: 4Spectral 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: 8Citation - Scopus: 8A New Method for Dissipative Dynamic Operator With Transmission Conditions(Springer Basel Ag, 2018) Ugurlu, Ekin; Tas, KenanIn 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.