Time and Band Limiting for Matrix Valued Functions, an Example
The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of p...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147111 |
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| Zitieren: | Time and Band Limiting for Matrix Valued Functions, an Example / F.A. Grünbaum, I. Pacharoni, I.N. Zurrián // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. |
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Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. 2019-02-13T16:51:23Z 2019-02-13T16:51:23Z 2015 Time and Band Limiting for Matrix Valued Functions, an Example / F.A. Grünbaum, I. Pacharoni, I.N. Zurrián // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 22E45; 33C47 DOI:10.3842/SIGMA.2015.044 https://nasplib.isofts.kiev.ua/handle/123456789/147111 The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing in a non-commutative setup that a bispectral property implies that the corresponding global operator of ''time and band limiting'' admits a commuting local operator. This is a noncommutative analog of the famous prolate spheroidal wave operator. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html. This research was supported in part by the Applied Mathematical Sciences subprogram of the Of fice of Energy Research, USDOE, under Contract DE-AC03-76SF00098, by AFOSR grant FA95501210087 through a subcontract to Carnegie Mellon University, by CONICET grant PIP 112-200801-01533, by SeCyT-UNC and by the Oberwolfach Leibniz Fellows Program. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Time and Band Limiting for Matrix Valued Functions, an Example Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Time and Band Limiting for Matrix Valued Functions, an Example |
| spellingShingle |
Time and Band Limiting for Matrix Valued Functions, an Example Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. |
| title_short |
Time and Band Limiting for Matrix Valued Functions, an Example |
| title_full |
Time and Band Limiting for Matrix Valued Functions, an Example |
| title_fullStr |
Time and Band Limiting for Matrix Valued Functions, an Example |
| title_full_unstemmed |
Time and Band Limiting for Matrix Valued Functions, an Example |
| title_sort |
time and band limiting for matrix valued functions, an example |
| author |
Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. |
| author_facet |
Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. |
| publishDate |
2015 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing in a non-commutative setup that a bispectral property implies that the corresponding global operator of ''time and band limiting'' admits a commuting local operator. This is a noncommutative analog of the famous prolate spheroidal wave operator.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147111 |
| citation_txt |
Time and Band Limiting for Matrix Valued Functions, an Example / F.A. Grünbaum, I. Pacharoni, I.N. Zurrián // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. |
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2025-12-01T12:02:52Z |
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2025-12-01T12:02:52Z |
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