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140122 ||| eng |
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|a 9783034854696
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|a Gohberg, I.
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|a Topics in Interpolation Theory of Rational Matrix-valued Functions
|h Elektronische Ressource
|c by I. Gohberg
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| 250 |
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|a 1st ed. 1988
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| 260 |
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|a Basel
|b Birkhäuser
|c 1988, 1988
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| 300 |
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|a IX, 247 p
|b online resource
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| 653 |
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|a Humanities and Social Sciences
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| 653 |
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|a Humanities
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| 653 |
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|a Social sciences
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Operator Theory: Advances and Applications
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| 028 |
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|a 10.1007/978-3-0348-5469-6
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| 856 |
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|u https://doi.org/10.1007/978-3-0348-5469-6?nosfx=y
|x Verlag
|3 Volltext
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|a 001.3
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|a 300
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|a 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
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