Topics in Interpolation Theory of Rational Matrix-valued Functions: 33 (Operator Theory: Advances and Applications) - Tapa blanda

Gohberg, I.

 
9783034854719: Topics in Interpolation Theory of Rational Matrix-valued Functions: 33 (Operator Theory: Advances and Applications)
Tapa blanda
ISBN 10: 3034854714 ISBN 13: 9783034854719
Editorial: Birkhäuser, 2014

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
2014
Idioma
Inglés
ISBN 10 
3034854714
ISBN 13 
9783034854719
Encuadernación
Tapa blanda
Número de páginas
260
Contacto del fabricante
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Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9783764322335: Topics in Interpolation Theory of Rational Matrix-valued Functions: v. 33 (Operator Theory: Advances and Applications)

Edición Destacada

ISBN 10:  3764322330 ISBN 13:  9783764322335
Editorial: Birkhauser Verlag AG, 1988
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