Constructive Methods of Wiener-Hopf Factorization (Operator Theory: Advances and Applications, 21)

Gohberg, Kaashoek

ISBN 10: 3034874200 / ISBN 13: 9783034874205

Edité par Birkhäuser, 2012

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N° de réf. du vendeur D8F0-0-M-3034874200-6

Détails bibliographiques

• Titre: Constructive Methods of Wiener-Hopf Factorization (Operator Theory: Advances and Applications, 21)
• Éditeur: Birkhäuser
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 3034874200
• ISBN à 13 chiffres: 9783034874205
• Reliure: Paperback
• État de l'article: Like New
• Type de livre: book

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Synopsis

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.