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Information × Registration Number 0223U002266, 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 A complete description of the extreme points of the set of measures on the unit circle, which carry out isometric nesting of finite-dimensional model spaces, is obtained. In the case of infinite-dimensional spaces, examples of extreme points with different spectral properties are given (singular measures, measures with a non-trivial absolutely continuous component). The existence of a singular measure in the Reichman class is proved. A bounded, closed, and convex set in the space of all sequences tending to zero, and an infinite number of functionals that reach a maximum of modulus on this set, are constructed. It is proved that the distributions on a-adic solenoids without elements of order 2, which are characterized by the symmetry of one linear form from two independent quantities while the other is fixed, are concatenations of Gaussian distributions and the distribution with a carrier in some subgroup. A complete description of locally compact abelian groups is found, on which the group analogue of Heyde's theorem holds in the case when the characteristic functions of the distributions do not converge to zero, and the coefficients of the linear forms are integers. A class of locally compact abelian groups is described for which A. Kagan's theorem holds, while the coefficients of linear forms are continuous endomorphisms of the group. A group analogue of the well-known Skytovych-Darmois theorem is proved in the case of three random independent quantities that take values in the group of p-adic numbers and three linear forms. Bounded cohomologies for ergodic nonsingular actions of amenable groups are studied. For each ergodic non-singular action of a counted amenable group, it is proved that the first cohomology group of the corresponding module of bounded dimensional functions with values in a finite dimensional vector space includes an ergodic class.  Product Description popup.authors popup.nrat_date 2023-02-14 Close