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Information × Registration Number 0307U001657, 0106U003143 , R & D reports Title Asymptotic methods in the function theory, operator functions, operator methods in the orbital theory popup.stage_title Властивості обмежених голоморфних в одиночному крузі функцій та матричні ортогональні многочлени. Head Grishin A., Registration Date 18-04-2007 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of research - contractive holomorphic on the unit disk complex-valued functions; systems of matricial orthogonal polynomials on the unit circle for general matrix-valued measures; bounded on the unit circle operator-valued functions. Purposes - to obtain quantitative criteria of the existence of the pseudocontinuation for complex-valued Schur functions; to construct and to investigate systems of matricial orthogonal polynomials for general matrix-valued measures on the unit circle; to obtain new properties of bounded on the unit circle operator-valued functions which are connected with regular factorizations. Methods of research - methods of real and complex analysis, methods of functional analysis. Results of research are applied to the study of Schur functions and operator-valued functions bounded on the unit circle. Results and methods of investigations can be applied in the research work of the following scientific bodies: the Institute of Physics and Engineering for Low Temperature of NAS of Ukraine, the Institute of Mathematics of NAS of Ukraine, the Universities of Donetsk, Kharkiv, Kyiv, Lviv, Moskow, Sankt Peterburg. KEY WORDS: SCHUR FUNCTION, SCHUR PARAMETERS, PSEUDOCONTINUATION, MATRICIAL ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE, BOUNDED ON THE UNIT CIRCLE OPERATOR-VALUED FUNCTIONS, REGULAR FACTORIZATIONS. Rules for receiving of the report: according to agreement. 61077, Kharkiv, Svobody sq., 4, Kharkiv national university. Product Description popup.authors popup.nrat_date 2020-04-02 Close