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Information × Registration Number 0213U006640, 0113U006061 , R & D reports Title Inverse problems in modern mathematical physics popup.stage_title Head Nizhnik Leonid Pavlovich, Доктор фізико-математичних наук Registration Date 18-12-2013 Organization Institute of mathematics NAS of Ukraine popup.description2 We propose and develope new explicitly solvable models for operators of quantum mechanics with non-local potentials. For Schrodinger operators with nonlocal potentials the inverse spectral problem is solved due to a new efficient algorithm. The Lax-Phillips approach in the scattering theory is extended onto the PT- symmetric operators, and it is shown that the indefinite metric that defines the inner product in a Krein space, in which the operator is self-adjoint is restored from the scattering matrix. Necessary and sufficient conditions for 1-dimensional Schrodinger operator with a singular matrix potential to be maximal accretive are obtained. The basic spectral theory of quasi-differential equations is constructed. Uniqueness theorems for the Cauchy problem are proved and the properties of solutions are investigated for the fractional diffusion- wave equations describing the propagation of waves in a viscoelastic medium. Precise conditions for asymptotic stability at infinity of solutions of evolution equations in Banach space are established. Based on a new concept of spectral polynomial the full spectral analysis of perturbed finite Jacobi matrices was conducted and its application to locally finite graphs is given. Product Description popup.authors Горбачук Валентина Іванівна Горбачук Мирослав Львович Горюнов Андрій Сергійович Грод Андрій Іванович Кочубей Анатолій Наумович Лебідь Вікторія Олександрівна Михайлець Володимир Андрійович Островський Василь Львович Рабанович Вячеслав Іванович Солодун Олександр Васильович popup.nrat_date 2020-04-02 Close