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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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
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1987
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina |
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paperaa:paper_0022247X_v125_n2_p331_Cortina2023-06-12T16:44:02Z On the multiplicity of Darlington realizations of contractive matrix-valued functions J. Math. Anal. Appl. 1987;125(2):331-350 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. 1987 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng 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) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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 |
Artículo Artículo publishedVersion |
| 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 |
| publishDate |
1987 |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v125_n2_p331_Cortina |
| work_keys_str_mv |
AT cortinae onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions AT dattellisce onthemultiplicityofdarlingtonrealizationsofcontractivematrixvaluedfunctions |
| _version_ |
1769810089877700608 |