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Information × Registration Number 0304U004085, 0103U004228 , R & D reports Title Subharmonic functions, operator functions, interpolation problems of analysis and ergodic theory popup.stage_title Опис усіх розширень голоморфних стискальних в одиночному крузі матриць-функцій до внутрішніх матриць-функцій у термінах відповідних операторів стиску Head Grishin A., Registration Date 20-03-2004 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of research - contractive holomorphic operator functions; contraction operators; unitary colligations and couplings; systems of orthogonal polynomials on the unit circle; scattering systems with discret and continuous time. Purposes - we go on to study holomorphic on the unit disk matrix functions; to study the problem of the construction for systems of polynomials on the unit circle to a full orthogonal systems in the case of Szego condition of unfullness; to obtain the criteria of regular divisibility for contractive operator-function in the class ; to investigate functions of the Caratheodory class as scattering matrices of the system with continuous time. Methods of research - the functions theory, the operator theory, the theory of unitary colligation and couplings, the theory of open systems. Results of research are applied to the study of holomorphic on the unit disk contractive matrix functions; to study of the systems of orthogonal polynomials on the unit circle; to the research of regular factorizations for contractive operator-function in the class ; to study of functions of the Caratheodory class. The results of investigations can be applied in the Institute of Physics and Engineering of Low temperature of NAS of Ukraine, in the Institute of Mathematics of NAS of Ukraine, in the universities of Kharkov, Simpheropol, Leipzig (Germany), South- Ukraine teacher university (c. Odessa). These results are exploited in special courses of the participators of this investigations. Product Description popup.authors popup.nrat_date 2020-04-02 Close