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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Autores principales: Cortina, E., D'Attellis, C.E.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0022247X_v125_n2_p331_Cortina2023-10-03T14:29:03Z On the multiplicity of Darlington realizations of contractive matrix-valued functions Cortina, E. D'Attellis, C.E. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Cortina, E.
D'Attellis, C.E.
spellingShingle Cortina, E.
D'Attellis, C.E.
On the multiplicity of Darlington realizations of contractive matrix-valued functions
author_facet Cortina, E.
D'Attellis, C.E.
author_sort Cortina, E.
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
url http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina
work_keys_str_mv AT cortinae onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions
AT dattellisce onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions
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