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Information × Registration Number 0203U008080, 0100U003351 , R & D reports Title Some questions of calculus popup.stage_title Head Grishin A., Registration Date 22-04-2003 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of research - subharmonic functions; holomorphic functions; meromorhic functions; meromorphic minimal surfaces; integrals with kernels depended on production of variables; contractive operators; contractive holomorphic functions; unitary coupling; dense embedding of diskrete group; nonsingular actions of abelian groups. Purposes - to construct general theory of growth of subharmonic in a half-plane functions; to prove more general version of the simplest taubertian theorem; to study integrals on a half-axis with kernels depended on production of variables; to study strong asymptotic places of meromorphic functions in the disk, to obtain one sharp estimate for magnitude of deviation of meromorphic minimal surface; to describe an algorithm of decomposition of Hellinger's space; to construct a model of contractive operators by its defect functions; to study pseudocontinuation of holomorphic contractive functions; to construct nonsingular action of countable abelian groups fanny 1-rank; to study dense embedding of free commutative group into noncompact locally compact groups; to investigate groups with property Z, to study actions of countable amenable groups. Methods of research - theory of subharmonic functions; theory of meromorhic functions; theory of dynamic system, theory of asymptotic evaluations, theory of operators; functional analysis, ergodic theory, theory of topological groups. Results of research are applied to the study of subharmonic functions in a half-plane, meromorphic functions in the disk, meromorphic minimal surfaces, integrals with kernels depended on production of variables, properties of Hellinger's space, properties of contractive operator, pseudocontinuation of holomorphic contractive functions, groups of ergodic transformations, dense subgroups of locally compact groups, groups with property Z, actions of countable amenable groups. The results of investigations can be applied in Institute of Mathematics of NAS of Ukraine, Institute of Mathematics of RAS, Institute for LowTemperature Physics and Engineering of NAS, in the universities of Beer-Sheve, Kharkiv, Kiev, Leipzig, Lviv, Odessa, Tel-Aviv, Torun. These results are exploited in special courses for mathematicians. Product Description popup.authors popup.nrat_date 2020-04-02 Close