Topics in Interpolation Theory of Rational Matrix-valued Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1988
|
| Schriftenreihe: | Operator Theory: Advances and Applications
33 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n |
| Beschreibung: | 1 Online-Ressource (IX, 247 p) |
| ISBN: | 9783034854696 9783034854719 |
| ISSN: | 0255-0156 |
| DOI: | 10.1007/978-3-0348-5469-6 |
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| 500 | |a One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_GND | (DE-588)118915878 |
| author_facet | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_role | aut |
| author_sort | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_variant | y z g yz yzg |
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| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 050 - General serial publications |
| dewey-raw | 50 |
| dewey-search | 50 |
| dewey-sort | 250 |
| dewey-tens | 050 - General serial publications |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-0348-5469-6 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
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| isbn | 9783034854696 9783034854719 |
| issn | 0255-0156 |
| language | English |
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| series2 | Operator Theory: Advances and Applications |
| spelling | Gohberg, Yiśrāʿēl Z. 1928-2009 Verfasser (DE-588)118915878 aut Topics in Interpolation Theory of Rational Matrix-valued Functions edited by I. Gohberg Basel Birkhäuser Basel 1988 1 Online-Ressource (IX, 247 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 33 0255-0156 One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n Science (General) Science, general Naturwissenschaft Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Rationale matrixwertige Funktion (DE-588)4201287-9 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Rationale matrixwertige Funktion (DE-588)4201287-9 s Interpolation (DE-588)4162121-9 s 1\p DE-604 Reelle Funktion (DE-588)4048918-8 s 2\p DE-604 Matrizenrechnung (DE-588)4126963-9 s 3\p DE-604 https://doi.org/10.1007/978-3-0348-5469-6 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 |
| spellingShingle | Gohberg, Yiśrāʿēl Z. 1928-2009 Topics in Interpolation Theory of Rational Matrix-valued Functions Science (General) Science, general Naturwissenschaft Matrizenrechnung (DE-588)4126963-9 gnd Interpolation (DE-588)4162121-9 gnd Rationale matrixwertige Funktion (DE-588)4201287-9 gnd Reelle Funktion (DE-588)4048918-8 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4162121-9 (DE-588)4201287-9 (DE-588)4048918-8 |
| title | Topics in Interpolation Theory of Rational Matrix-valued Functions |
| title_auth | Topics in Interpolation Theory of Rational Matrix-valued Functions |
| title_exact_search | Topics in Interpolation Theory of Rational Matrix-valued Functions |
| title_full | Topics in Interpolation Theory of Rational Matrix-valued Functions edited by I. Gohberg |
| title_fullStr | Topics in Interpolation Theory of Rational Matrix-valued Functions edited by I. Gohberg |
| title_full_unstemmed | Topics in Interpolation Theory of Rational Matrix-valued Functions edited by I. Gohberg |
| title_short | Topics in Interpolation Theory of Rational Matrix-valued Functions |
| title_sort | topics in interpolation theory of rational matrix valued functions |
| topic | Science (General) Science, general Naturwissenschaft Matrizenrechnung (DE-588)4126963-9 gnd Interpolation (DE-588)4162121-9 gnd Rationale matrixwertige Funktion (DE-588)4201287-9 gnd Reelle Funktion (DE-588)4048918-8 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Matrizenrechnung Interpolation Rationale matrixwertige Funktion Reelle Funktion |
| url | https://doi.org/10.1007/978-3-0348-5469-6 |
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