Allahverdiev, Bilender P.Uğurlu, EkinUgurlu, EkinMatematik2025-09-232025-09-232017Allahverdiev, Bilender P.; Ugurlu, Ekin, "Scattering and spectral problems of the direct sum sturm-liouville operators", Applied And Computational Mathematics, Vol.16, No.3, pp.257-268, (2017).1683-35111683-6154https://hdl.handle.net/20.500.12416/15529In this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.eninfo:eu-repo/semantics/closedAccessDirect Sum OperatorsDissipative OperatorsScattering TheoryFunctional ModelSpectral AnalysisArticle2-s2.0-85048572267