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Information × Registration Number 0223U002263, 0118U003110 , R & D reports Title Methods of the functions theory in spectral theory, control theory, functional equations, ergodic theory, and representation theory popup.stage_title Head Feldman Hennadii M., д.ф.-м.н. Registration Date 14-02-2023 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2 The stability of the Borg-Hochstadt theorem in the theory of periodic Jacobian matrices is studied. Two-sided estimates of the lengths of gaps in the spectrum of such matrices were obtained. Estimates of the Lebesgue measure of the spectrum of the (p1,p2)-periodic operator have been established. A description of the spectra of comb-type graphs, both finite combs and finite combs with an infinite ray attached to one vertex, is found. The main properties of the scattering coefficient are established for the Dirac operator. It is shown that according to the scattering coefficient, not all disturbance elements are uniquely located. A class of problems for which such recovery is unambiguous is described. The heat conduction equation on the semi-axis governed by the Dirichlet boundary condition was investigated. In terms of the solvability of the power-law problem of Markov moments for any initial state of the controlled system, the controllability criterion for a given time is obtained. It is proved that any initial state of the system is approximately controllable for any given time. An algorithm for constructing a control that solves the problem of approximate controllability in a given time is developed and illustrated with examples. Controllability problems for the degenerate wave equation with variable coefficients are studied. An analogue of Heyde's theorem is proved for discrete abelian groups. A characterization theorem is proved that characterizes the shifts of the Haar distributions of compact subgroups of a completely disconnected locally compact field. A number of characterization theorems for Q-independent random variables on groups are proved. The well-known Koslov's theorem on non-semistationary shifts has been strengthened. An example of a weakly mixing nonsingular Bernoulli shift, which does not admit an equivalent semistationary measure, is constructed.  Product Description popup.authors popup.nrat_date 2023-02-14 Close