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

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, Elsa Aurora, D'Attellis, Carlos Enrique
Publicado: 1987
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v125_n2_p331_Cortina
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
id paper:paper_0022247X_v125_n2_p331_Cortina
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spelling paper:paper_0022247X_v125_n2_p331_Cortina2023-06-08T14:47:45Z On the multiplicity of Darlington realizations of contractive matrix-valued functions Cortina, Elsa Aurora D'Attellis, Carlos Enrique 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. Fil:Cortina, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:D'Attellis, C.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1987 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v125_n2_p331_Cortina http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
author Cortina, Elsa Aurora
D'Attellis, Carlos Enrique
spellingShingle Cortina, Elsa Aurora
D'Attellis, Carlos Enrique
On the multiplicity of Darlington realizations of contractive matrix-valued functions
author_facet Cortina, Elsa Aurora
D'Attellis, Carlos Enrique
author_sort Cortina, Elsa Aurora
title On the multiplicity of Darlington realizations of contractive matrix-valued functions
title_short On the multiplicity of Darlington realizations of contractive matrix-valued functions
title_full On the multiplicity of Darlington realizations of contractive matrix-valued functions
title_fullStr On the multiplicity of Darlington realizations of contractive matrix-valued functions
title_full_unstemmed On the multiplicity of Darlington realizations of contractive matrix-valued functions
title_sort on the multiplicity of darlington realizations of contractive matrix-valued functions
publishDate 1987
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v125_n2_p331_Cortina
http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina
work_keys_str_mv AT cortinaelsaaurora onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions
AT dattelliscarlosenrique onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions
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