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Information × Registration Number 0200U003568, 0197U015783 , R & D reports Title Some questions of the mathematical analysis and their applications to complex systems of Quatum Mechanics. popup.stage_title Head Gryshyn A.P., Registration Date 08-06-2000 Organization Kharkov National University named after V.N. Karazin popup.description2 Object of reseach - harmonic and subharmonic functions; contractive operators, pseudocontinuation of holomorfic contractive functions; descrete groups with nhe property Z; cocycles of ergodic transformations. Purposes - We go on to construct a version of the Nevanlinna theory for the complex half - plane, to study limiting values of the indicators of subharmonic functions in the half-plane, to construct and study the model of contractive operator that generate unilateral shift, to resolve extremal problem for contractive harmonic operator's functions in the unit disc; to study the class of descrete groups with property Z and to give the complete describing of the descrete commutative groups with the property Z ; to reseach a structure of centralizator of the ergodic extensions of measurable transformations; to find complete system of invariants of the quasyorder for the set of cocycles of ergodic hyperfinite relation of equivalents. Methods of reseach are the ones of the theory func tions, theory of operators, the functional analysis and the ergodic theory. Results of reseach are applyed to the stude of properties of harmonic and subharmonic functions, of properties of contractive operators, to the discription of ergodic transformations and cocycles of hyperfinite relations of equivalence. Product Description popup.authors popup.nrat_date 2020-04-03 Close