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Time and Band Limiting for Matrix Valued Functions, an Example
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Time and Band Limiting for Matrix Valued Functions, an Example
Інший ID:
2010 Mathematics Subject Classification: 33C45; 22E45; 33C47
DOI:10.3842/SIGMA.2015.044
DOI:10.3842/SIGMA.2015.044
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
540
Завантажень:
174
Анотація:
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.
