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Characterization problems on abelian groups, spectral multiplicities of ergodic actions and classification of measures on Cantor spaces

Work number - M 14 FILED


KarpelO.M.,MyronyukM.V., SolomkoA.V.

We proved characterization theorems on groups. In particular, we obtained the analogues of  the Kac-Bernstein theorem on cylinder and a-adic solenoid, analogue of Skitovich-Darmoit theorem on cylinders, analogues of  Heyde’s theorem on discrete group and in Banach spase.

ThecriterionisprovedforprobabilityinvariantergodicmeasuresonthepathspacesofstationaryBrattelidiagramstobehomeomorphic. The criterion of topological equivalence for infinite non-defective Borel measures on a compact Cantor space is obtained, together with the criterion for measures on a non-compact locally compact Cantor set to be homeomorphic.

In the field of spectral theory of dynamical systems we extended the recent progress achieved by O. Ageev, V. Ryzhikov and A. Danilenko to substantially more general class of abelian locally compact group actions.In particular, we proved the existence of actions with homogeneous spectrum. Answering a question of C. Silva, we constructed a family of infinite measure preserving flows with infinite ergodic index.

The results of the series of the works are published in 11 articles (including 9 in foreign journals). 10 articles are published in journals with positive impact factor, the average impact factor is 0,589.

The total number of the authors’ publications : 24 articlesand20 conference theses.