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Information × Registration Number 0209U001074, 0106U008147 , R & D reports Title Spectral theory of some classes of singularly perturbed operators popup.stage_title Head Derkach Volodymyr Oleksandrovich, Registration Date 12-01-2009 Organization Donetsk National University popup.description2 General boundary value problems with non-degenerate characteristic determinant for the Sturm-Lioville equation on a finite interval are investigated. Necessary and sufficient conditions for the completeness of root vectors are obtained in terms of the potential. An explicit formula for the scattering matrix of two self-adjoint extensions of a symmetric operator is obtained in terms of the Weyl function. An analog of the de Leeuw and Mirkil theorem for operators with variable coefficients is obtained. Wide classes of weakly coercive but not elliptic systems with constant coefficients are constructed.. It is shown that a J-nonnegative Sturm-Liouville operator with a model indefinite weight r(x)=sgn x may have a singular critical point 0. Sufficient conditions for the similarity of the Volterra operators in the Lebesgue space of vector-functions are studied. Product Description popup.authors popup.nrat_date 2020-04-02 Close