Search academic texts

Information × Registration Number 0223U002142, 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 11-02-2023 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2 Blaschke-type conditions are obtained for functions belonging to a wider class than the class that was known before. This result was applied to the study of perturbations of linear operators. It is proved that the non-radial growth of the perturbation determinant is a consequence of the nature of the growth of the Biermann-Schwinger operator for the unperturbed operator. The accuracy of the spectral XYZ theorem is proved. We obtained exact polynomial two-sided estimates of the norms of certain classes of strongly continuous groups and proved that these groups do not have any maximal asymptotics. Kato's theorem on the stability of Riesz bases for the case of non-self-adjoint projectors is generalized. A new generalization of the Skitovich-Darmois characterization theorem for arbitrary locally compact abelian groups containing a subgroup that is topologically isomorphic to the circle rotation group, but not containing a subgroup that is topologically isomorphic to a two-dimensional torus, is obtained. An analogue of S.R. Rao's theorems is proved for linear forms of independent random variables taking values in a locally compact abelian group, as well as for independent random variables taking values in an a-adic solenoid. In this case, the coefficients of linear forms are continuous endomorphisms of the group. Using the Kesten-Spitzer theorem, necessary and sufficient conditions for the recurrence of random walks on arbitrary subgroups of the group of rational numbers that are not isomorphic to the group of integers are found. The elements of the general theory of joinings for ergodic homeomorphisms T of a locally compact non-compact Cantor space endowed with an infinite (nonatomic) sigma cfinite ergodic Radon T-invariant measure have been developed.  Product Description popup.authors popup.nrat_date 2023-02-11 Close