Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Dissipative Operator and Its Cayley Transform(Tubitak Scientific & Technological Research Council Turkey, 2017) Ugurlu, Ekin; Tas, KenanIn this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C-0. Using Solomyak's method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.Article Dirac Systems with Regular and Singular Transmission Effects(Tubitak Scientific & Technological Research Council Turkey, 2017) Ugurlu, EkinIn this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl's limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax-Phillips scattering function and Sz-Nagy-Foias characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.Article A First-Order System of Equations on a Compact Star Graph(Ankara Univ, FAC Sci, 2025) Mutlu, Gokhan; Ugulu, Ekin; Uğurlu, EkinThis study concerns a boundary value problem generated by a system of first-order differential equations and some symmetric boundary conditions on a compact star graph. Unlike usual quantum graph Hamiltonians, the Hamiltonian considered in this paper acts on vector-valued functions living on the edges. Appropriate vertex conditions are introduced to ensure the corresponding boundary value problem is symmetric. In particular, coupling and separated conditions are imposed at the central and boundary vertices, respectively. Moreover, the general form of the vertex conditions at the central vertex is discussed. Finally, the characteristic function is constructed for the symmetric boundary value problem generated by the first-order system and specific coupling vertex conditions.Article Citation - WoS: 3Citation - Scopus: 5Coordinate-Free Approach for the Model Operator Associated With a Third-Order Dissipative Operator(Frontiers Media Sa, 2019) Ugurlu, Ekin; Baleanu, DumitruIn this paper we investigate the spectral properties of a third-order differential operator generated by a formally-symmetric differential expression and maximal dissipative boundary conditions. In fact, using the boundary value space of the minimal operator we introduce maximal selfadjoint and maximal non-selfadjoint (dissipative, accumulative) extensions. Using Solomyak's method on characteristic function of the contractive operator associated with a maximal dissipative operator we obtain some results on the root vectors of the dissipative operator. Finally, we introduce the selfadjoint dilation of the maximal dissipative operator and incoming and outgoing eigenfunctions of the dilation.