Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1The Spectral Analysis of a System of First-Order Equations With Dissipative Boundary Conditions(Wiley, 2021) Ugurlu, EkinThis 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: 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.