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...
Gespeichert in:
| Datum: | 2015 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2015
|
| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147111 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147111 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
irk-123456789-1471112019-02-14T01:23:17Z Time and Band Limiting for Matrix Valued Functions, an Example Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147111 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. |
| spellingShingle |
Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. Time and Band Limiting for Matrix Valued Functions, an Example Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Grünbaum, F.A. Pacharoni, I. Zurrián, I.N. |
| author_sort |
Grünbaum, F.A. |
| title |
Time and Band Limiting for Matrix Valued Functions, an Example |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT grunbaumfa timeandbandlimitingformatrixvaluedfunctionsanexample AT pacharonii timeandbandlimitingformatrixvaluedfunctionsanexample AT zurrianin timeandbandlimitingformatrixvaluedfunctionsanexample |
| first_indexed |
2025-07-11T01:23:16Z |
| last_indexed |
2025-07-11T01:23:16Z |
| _version_ |
1837311720539815936 |