Raul E. Curto, In Sung Hwang, Woo Young Lee Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory 9781470436247

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Автор: Raul E. Curto, In Sung Hwang, Woo Young Lee
Название: Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
ISBN: 9781470436247
Издательство: Mare Nostrum (Eurospan)
Классификация:

Основы высшей математики и математический анализ

ISBN-10: 1470436248
Обложка/Формат: Paperback
Страницы: 100
Вес: 0.21 кг.
Дата издания: 30.10.2019
Серия: Memoirs of the american mathematical society
Язык: English
Размер: 177 x 251 x 12
Читательская аудитория: Professional and scholarly
Ключевые слова: Calculus & mathematical analysis
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Поставляется из: Англии
Описание: In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejer Interpolation Problem for matrix rational functions.The authors then extend the $H^\infty$-functional calculus to an $\overline{H^\infty}+H^\infty$-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmoss Problem 5 and then establish a matrix-valued version of Abrahamses Theorem. They also solve a subnormal Toeplitz completion problem of $2\times 2$ partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.
Дополнительное описание: Calculus and mathematical analysis

Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory, Raul E. Curto, In Sung Hwang, Woo Young Lee