| Topics in Interpolation Theory of Rational Matrix-Valued Functions Softcover Repri Edition Contributor(s): Gohberg, I. (Author) |
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ISBN: 3034854714 ISBN-13: 9783034854719 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: August 2014 |
| Additional Information |
| BISAC Categories: - Science - Reference - Non-classifiable |
| Dewey: 050 |
| Series: Operator Theory: Advances and Applications |
| Physical Information: 0.55" H x 6.69" W x 9.61" (0.92 lbs) 247 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl, " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . ., m, and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj: f: wk(1 j 1, 1 k p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l (2) J ( Z+ Zj where o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp: f: - Zq for 1 ]1, q n. |