Matematik Bölümü Yayın Koleksiyonu

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

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2015 - 20162

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Author: search.filters.author.Allahverdiev, Bilender P.Subject: search.filters.subject.Dissipative Operator

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  • 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: 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.