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Information × Registration Number 0223U002268, 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 It was established that the non-local potential is restored by three spectra, while the corresponding equations describe the behavior of particles on the crystal surface, which makes it possible to restore the structure of the crystal surface by these spectra. It is proved that for a class of linear control systems with time delay that satisfy the complementarity property of generalized eigenvectors, the problems of full stabilization and exact zero controllability are equivalent. A complete description of completely disconnected compact Abelian groups for which Heyde's theorem holds is found. Characteristic theorems of Skytovich-Darmois and Heyde for complex random variables are proved. The main characterization theorems for distributions of Q-independent random variables with values in the Banach space are proved. A group analogue of the generalized Poya theorem is proved, in which the Gaussian distribution is characterized by the same distribution of the monomial and the linear form of independent identically distributed random variables. At the same time, the coefficients of the linear form are the topological automorphisms of the group. A complete description of the solutions of the Katz-Bernstein functional equation on an arbitrary abelian group in the class of positive functions and in the class of functions satisfying the Hermitity condition is found. An analogue of de Finetti's theorem was obtained for infinite symmetric groups, which are inductive limits of finite symmetric groups with diagonal nesting. Using the Perron-Frobenius theory for infinite matrices, ergodic finite and sigma finite measures on the path space of generalized Brattel diagrams, which are invariant with respect to the cofinite equivalence relation, are found.  Product Description popup.authors popup.nrat_date 2023-02-14 Close