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Constructive Methods of Wiener-Hopf Factorization. Softcover reprint of the original 1st ed. 1986.
・ISBN 978-3-0348-7420-5 paper EUR 49.99
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| 著者・編者 | Gohberg / Kaashoek, |
|---|---|
| シリーズ | Operator Theory: Advances and Applications |
| 出版社 | (Springer Basel, SZ) |
| 出版年月 | 2012 |
| ページ数 | 410 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-18383＞ |
解説
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.