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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Datum: | 2015 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | English |
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Інститут математики НАН України
2015
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Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147111 |
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Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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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Digital Library of Periodicals of National Academy of Sciences of UkraineZusammenfassung: | 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. |
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