On the multiplicity of Darlington realizations of contractive matrix-valued functions

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We obtain a unique expression for a Darlington realization of a contractive matrix-valued function S(z)ε{lunate}Lτ, valid for the three following cases: (a)S(z) is inner: (b) S(z) is not inner and det[In - S*(ξ) S(ξ)] ≠ 0 a.e.: (c) S(z) is not inner and det[In - S*( 1 z) S(z)] = 0 (z ε{lunate} D). O...

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Detalles Bibliográficos
Autores principales: Cortina, E., D'Attellis, C.E.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 1987
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We obtain a unique expression for a Darlington realization of a contractive matrix-valued function S(z)ε{lunate}Lτ, valid for the three following cases: (a)S(z) is inner: (b) S(z) is not inner and det[In - S*(ξ) S(ξ)] ≠ 0 a.e.: (c) S(z) is not inner and det[In - S*( 1 z) S(z)] = 0 (z ε{lunate} D). On the basis of this result we examinate the problem of multiplicity of realizations for the case (c). © 1987.

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