Constructive Methods of Wiener-Hopf Factorization
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1986
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| Schriftenreihe: | OT 21: Operator Theory: Advances and Applications
21 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Beschreibung: | 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 |
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| Beschreibung: | 1 Online-Ressource (XII, 410 p) |
| ISBN: | 9783034874182 9783034874205 |
| DOI: | 10.1007/978-3-0348-7418-2 |