Extension and Interpolation of Linear Operators and Matrix Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
1990
|
| Series: | Operator Theory: Advances and Applications
47 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . |
| Physical Description: | 1 Online-Ressource (VII, 305 p) |
| ISBN: | 9783034877015 9783764325305 |
| DOI: | 10.1007/978-3-0348-7701-5 |
Staff View
MARC
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Record in the Search Index
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| author | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_GND | (DE-588)118915878 |
| author_facet | Gohberg, Yiśrāʿēl Z. 1928-2009 |
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| bvnumber | BV042421956 |
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| dewey-full | 50 |
| dewey-hundreds | 000 - Computer science, information, general works |
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| dewey-raw | 50 |
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| dewey-sort | 250 |
| dewey-tens | 050 - General serial publications |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7701-5 |
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| id | DE-604.BV042421956 |
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| indexdate | 2024-07-10T01:21:10Z |
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| language | English |
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| spelling | Gohberg, Yiśrāʿēl Z. 1928-2009 Verfasser (DE-588)118915878 aut Extension and Interpolation of Linear Operators and Matrix Functions edited by I. Gohberg Basel Birkhäuser Basel 1990 1 Online-Ressource (VII, 305 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 47 The classicallossless inverse scattering (LIS) problem of network theory is to find all possible representations of a given Schur function s(z) (i. e. , a function which is analytic and contractive in the open unit disc D) in terms of an appropriately restricted class of linear fractional transformations. These linear fractional transformations corre spond to lossless, causal, time-invariant two port networks and from this point of view, s(z) may be interpreted as the input transfer function of such a network with a suitable load. More precisely, the sought for representation is of the form s(Z) = -{ -A(Z)SL(Z) + B(z)}{ -C(Z)SL(Z) + D(z)} -1 , (1. 1) where "the load" SL(Z) is again a Schur function and _ [A(Z) B(Z)] 0( ) (1. 2) Z - C(z) D(z) is a 2 x 2 J inner function with respect to the signature matrix This means that 0 is meromorphic in D and 0(z)* J0(z) ::5 J (1. 3) for every point zED at which 0 is analytic with equality at almost every point on the boundary Izi = 1. A more general formulation starts with an admissible matrix valued function X(z) = [a(z) b(z)] which is one with entries a(z) and b(z) which are analytic and bounded in D and in addition are subject to the constraint that, for every n, the n x n matrix with ij entry equal to X(Zi)J X(Zj )* i,j=l, . . Science (General) Science, general Naturwissenschaft Interpolation (DE-588)4162121-9 gnd rswk-swf Matrixfunktion (DE-588)4169117-9 gnd rswk-swf Erweiterung (DE-588)4128080-5 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Entwicklung (DE-588)4113450-3 gnd rswk-swf Matrixfunktion (DE-588)4169117-9 s Entwicklung (DE-588)4113450-3 s Interpolation (DE-588)4162121-9 s 1\p DE-604 Linearer Operator (DE-588)4167721-3 s 2\p DE-604 Erweiterung (DE-588)4128080-5 s 3\p DE-604 4\p DE-604 Matrizenrechnung (DE-588)4126963-9 s 5\p DE-604 https://doi.org/10.1007/978-3-0348-7701-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gohberg, Yiśrāʿēl Z. 1928-2009 Extension and Interpolation of Linear Operators and Matrix Functions Science (General) Science, general Naturwissenschaft Interpolation (DE-588)4162121-9 gnd Matrixfunktion (DE-588)4169117-9 gnd Erweiterung (DE-588)4128080-5 gnd Linearer Operator (DE-588)4167721-3 gnd Matrizenrechnung (DE-588)4126963-9 gnd Entwicklung (DE-588)4113450-3 gnd |
| subject_GND | (DE-588)4162121-9 (DE-588)4169117-9 (DE-588)4128080-5 (DE-588)4167721-3 (DE-588)4126963-9 (DE-588)4113450-3 |
| title | Extension and Interpolation of Linear Operators and Matrix Functions |
| title_auth | Extension and Interpolation of Linear Operators and Matrix Functions |
| title_exact_search | Extension and Interpolation of Linear Operators and Matrix Functions |
| title_full | Extension and Interpolation of Linear Operators and Matrix Functions edited by I. Gohberg |
| title_fullStr | Extension and Interpolation of Linear Operators and Matrix Functions edited by I. Gohberg |
| title_full_unstemmed | Extension and Interpolation of Linear Operators and Matrix Functions edited by I. Gohberg |
| title_short | Extension and Interpolation of Linear Operators and Matrix Functions |
| title_sort | extension and interpolation of linear operators and matrix functions |
| topic | Science (General) Science, general Naturwissenschaft Interpolation (DE-588)4162121-9 gnd Matrixfunktion (DE-588)4169117-9 gnd Erweiterung (DE-588)4128080-5 gnd Linearer Operator (DE-588)4167721-3 gnd Matrizenrechnung (DE-588)4126963-9 gnd Entwicklung (DE-588)4113450-3 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Interpolation Matrixfunktion Erweiterung Linearer Operator Matrizenrechnung Entwicklung |
| url | https://doi.org/10.1007/978-3-0348-7701-5 |
| work_keys_str_mv | AT gohbergyisraʿelz extensionandinterpolationoflinearoperatorsandmatrixfunctions |