Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Scopus Q: search.filters.scopusQuartile.Q2Subject: search.filters.subject.Spectral Analysis

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Now showing 1 - 4 of 4
  • 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: 2
    Citation - Scopus: 2
    Singular Dissipative Third-Order Operator and Its Characteristic Function
    (Springer Basel Ag, 2020) Ugurlu, Ekin
    In 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: 9
    Citation - Scopus: 10
    Extensions of a Minimal Third-Order Formally Symmetric Operator
    (Malaysian Mathematical Sciences Soc, 2020) Ugurlu, Ekin
    In this paper, we consider some regular boundary value problems generated by a third-order differential equation and some boundary conditions. In particular, we construct maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal operator. Further using Lax-Phillips scattering theory and Sz.-Nagy-Foias characteristic function theory we prove a completeness theorem.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Investigation of the Eigenvalues and Root Functions of the Boundary Value Problem Together With a Transmission Matrix
    (Taylor & Francis Ltd, 2020) Ugurlu, Ekin
    In this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.