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.
General
Imprint: |
Springer Basel
|
Country of origin: |
Switzerland |
Series: |
Operator Theory: Advances and Applications, 21 |
Release date: |
April 2012 |
First published: |
1986 |
Authors: |
Gohberg
• Kaashoek
|
Dimensions: |
244 x 170 x 21mm (L x W x T) |
Format: |
Paperback
|
Pages: |
410 |
Edition: |
Softcover reprint of the original 1st ed. 1986 |
ISBN-13: |
978-3-03-487420-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Calculus & mathematical analysis >
General
|
LSN: |
3-03-487420-0 |
Barcode: |
9783034874205 |
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