ISBN: 9783034854719 - topics in interpolation theory of rational matrix-valued functions: 33 (13 risultati)

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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 247 pp. Englisch.…

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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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, th.…

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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 260 pp. Englisch.…