### Abstract

We shall investigate two uncertainty principles for the Cherednik transform on the Euclidean space a; Miyachi's theorem and Beurling's theorem. We give an analogue of Miyachi' theorem for the Cherednik transform and under the assumption that o has a hypergroup structure, an analogue of Beurling's theorem for the Cherednik transform.

Original language | English |
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Pages (from-to) | 429-436 |

Number of pages | 8 |

Journal | Proceedings of the Indian Academy of Sciences: Mathematical Sciences |

Volume | 122 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 Aug |

### Fingerprint

### Keywords

- Beurling's theorem
- Cherednik operators
- Cherednik transform
- Miyachi's theorem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Indian Academy of Sciences: Mathematical Sciences*,

*122*(3), 429-436. https://doi.org/10.1007/s12044-012-0079-2

**Uncertainty principles for the Cherednik transform.** / Daher, R.; Hamad, S. L.; Kawazoe, Takeshi; Shimeno, N.

Research output: Contribution to journal › Article

*Proceedings of the Indian Academy of Sciences: Mathematical Sciences*, vol. 122, no. 3, pp. 429-436. https://doi.org/10.1007/s12044-012-0079-2

}

TY - JOUR

T1 - Uncertainty principles for the Cherednik transform

AU - Daher, R.

AU - Hamad, S. L.

AU - Kawazoe, Takeshi

AU - Shimeno, N.

PY - 2012/8

Y1 - 2012/8

N2 - We shall investigate two uncertainty principles for the Cherednik transform on the Euclidean space a; Miyachi's theorem and Beurling's theorem. We give an analogue of Miyachi' theorem for the Cherednik transform and under the assumption that o has a hypergroup structure, an analogue of Beurling's theorem for the Cherednik transform.

AB - We shall investigate two uncertainty principles for the Cherednik transform on the Euclidean space a; Miyachi's theorem and Beurling's theorem. We give an analogue of Miyachi' theorem for the Cherednik transform and under the assumption that o has a hypergroup structure, an analogue of Beurling's theorem for the Cherednik transform.

KW - Beurling's theorem

KW - Cherednik operators

KW - Cherednik transform

KW - Miyachi's theorem

UR - http://www.scopus.com/inward/record.url?scp=84866638980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866638980&partnerID=8YFLogxK

U2 - 10.1007/s12044-012-0079-2

DO - 10.1007/s12044-012-0079-2

M3 - Article

AN - SCOPUS:84866638980

VL - 122

SP - 429

EP - 436

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

SN - 0253-4142

IS - 3

ER -