TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS Таврический Вестник Информатики и Математики 1729-3901 54980 10.29039/1729-3901-2021-20-1-32-47 Основная рубрика Main category Основная рубрика Connection between the inverse Schur transformation for generalized Nevanlinna functions with the rational matrix functions of special type Связь обратного преобразования Шура обобщённого класса Неванлинны с рациональными матричными функциями специального вида Андреищева Елена Николаевна Andreischeva Elena Nikolaevna Черноморское высшее военно-морское училище им. П.С. Нахимова Россия Черноморское высшее военно-морское училище им. П.С. Нахимова Russian Federation 25 11 2022 25 11 2022 1 32 47 09 11 2022 http://tvim.info/node/1049

В статье рассматривается понятие обратного преобразования Шура для обобщенных функций класса Неванлинны. Связь между преобразованием Шура и разложением ttt-матричных функций основана на том факте, что для обобщенных функций Неванлинны матричные функции qz, соответствующие обратному преобразованию Шура, являются элементарными Jel-унитарными множителями. Минимальное разложение данной рациональной Jel-унитарной ttt-матричной функции qz может быть получено путем многократного применения преобразования Шура, что мы называем алгоритмом Шура.

In this paper we consider classical Schur transformation and inverse Schur transformation for generalized Nevanlinna functions.

 индефинитная метрика пространство Понтрягина функция Неванлинны преобразование Шура воспроизводящее ядро факторизация рациональных матричных функций indefinite metrics Nevanlinna function Pontryagin space Schur transformation reproducing kernel factorization of rational matrix function.

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