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Information × Registration Number 0216U005382, 0111U001027 , R & D reports Title Evolution and spectral problems for differential equations in a Banach space. popup.stage_title Head Gorbachuk Myroslav L'vovych, Registration Date 22-01-2016 Organization Institute of mathematics NAS of Ukraine popup.description2 The purpose of the work is to develop new approaches to constructing the exact and approximate solutions of the evolutionary and spectral problems for operator-differential equations and to applicate them to concrete problems of the mathematical physics, in partial, to investigation of solutions for the evolutionary equations of quantum multi-particle systems and PT-symmetric quantum mechanics, the development of new directions in the theory of groups of operators in a Banach space, the theory of extensions of symmetric operators in spaces with indefinite metrics, the quantum field theory, the theory of changeable sets. The main results: 1) the solution of the well-known Kolmogorov problem on the representation of a continuous group of linear operators in a Banach space by a power series; 2) the solution of the Hille problem on the description of the set of vectors in a Banach space where a group of linear operators acting on this space may be represented in the form of exponential of its generator; 3) the development of methods of strict verification of nonlinear kinetic equations of many particles and the investigation of asymptotical properties of their solutions on the Bolzman-Gred boundary; 4) the development of the theory of changeable and kinematic changeable sets; 5) the spectral analysis of the two-dimensional Shredinger operator. Product Description popup.authors Артемиченко Ж.Я. Герасименко В.І. Горбачук В.І. Горбачук М.Л. Грод А.І. Грушка Я.І. Золотенко Г.Ф. Кужель С.О. Пацюк О.М. Рябуха Т.В. Торба С.І. popup.nrat_date 2020-04-02 Close