WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article A Left-Definite Non-Integer-Order Dissipative Operator(Springer Nature, 2026) Ugurlu, EkinIn this paper we consider a non-integer (fractional)-order nonselfadjoint boundary-value problem so that the fractional-order equation is a kind of left-definite equation. We construct a dissipative operator in a Sobolev space H-1(a,b) and we introduce several results on the spectral properties of the related operators. In particular, we construct an inverse operator with the aid of the Dirac-delta function and we apply Krein's theorem to the inverse operator which is compact having a nuclear imaginary component.Article Variational Approach To a Symmetric Boundary Value Problem Generated by a System of Equations and Separated Boundary Conditions(Wiley, 2024) Ugurlu, EkinThis work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second-order Sturm-Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are complete in mean and energy. We introduce the results using the variational approach that enables us to consider only continuous pair functions instead of absolutely continuous pair functions.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: 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: 5Citation - Scopus: 5The Spectral Analysis of a Nuclear Resolvent Operator Associated With a Second Order Dissipative Differential Operator(Springer Heidelberg, 2017) Bairamov, Elgiz; Ugurlu, EkinIn 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.