I. Gohberg Extension and Interpolation of Linear Operators and Matrix Functions 9783764325305

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Автор: I. Gohberg
Название: Extension and Interpolation of Linear Operators and Matrix Functions
ISBN: 9783764325305
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

ISBN-10: 3764325305
Обложка/Формат: Hardcover
Страницы: 305
Вес: 0.42 кг.
Дата издания: 01.10.1990
Серия: Operator Theory: Advances and Applications
Язык: English
Размер: 229 x 152 x 17
Основная тема: Science, Humanities and Social Sciences, multidisciplinary
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e., a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre- spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1, (1. 1) where the load SL(Z) is again a Schur function and _ A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z)::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i, j=l, . . .

Extension and Interpolation of Linear Operators and Matrix Functions, I. Gohberg