Constructive Methods of Wiener-Hopf Factorization

von Gohberg, Kaashoek

410 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

The main part of this paper concerns Toeplitz operators of which the symbol W is an m x m matrix function defined on a disconnected curve r. The curve r is assumed to be the union of s + 1 nonintersecting simple smooth closed contours rOo r •. . . • rs which form the positively l oriented boundary of a finitely connected bounded domain in t. Our main requirement on the symbol W is that on each contour rj the function W is the restriction of a rational matrix function Wj which does not have poles and zeros on rj and at infinity. Using the realization theorem from system theory (see. e. g . • [1]. Chapter 2) the rational matrix function Wj (which differs from contour to contour) may be written in the form 1 (0. 1) W . (A) = I + C. (A - A. f B. A E r· J J J J J where Aj is a square matrix of size nj x n• say. B and C are j j j matrices of sizes n. x m and m x n . • respectively. and the matrices A. J x J J and Aj = Aj - BjC have no eigenvalues on r . (In (0. 1) the functions j j Wj are normalized to I at infinity.

• Reihe: Operator Theory: Advances and Applications
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein
• ISBN: 9783034874205
• Sprache: Englisch
• Erscheinungsdatum: 19.04.2012
• Größe: 24.4 x 17 cm
• Verlag: Springer Basel