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| 題 名 | q-Analogue of the Dunkl Transform on the Real Line |
|---|---|
| 作 者 | Bettaibi, Néji; B3ttaieb, Rym; | 書刊名 | Tamsui Oxford Journal of Mathematical Sciences |
| 卷 期 | 25:2 2009.05[民98.05] |
| 頁 次 | 頁177-205 |
| 分類號 | 314.16 |
| 關鍵詞 | q-Dunkl operator; q-Dunkl transform; q-Dunkl intertwining operator; |
| 語 文 | 英文(English) |
| 英文摘要 | In this paper, we consider a q-analogue of the Dunkl operator on R, we define and study its associated Fourier transform which is a q-analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this q-Dunkl transform. Next, we study the q-Dunkl intertwining operator and its dual via the q-analogues of the Riemann-Liouville and Weyl transforms. Using this dual intertwining operator, we provide a relation between the q-Dunkl transform and the q²-analogue Fourier transform introduced and studied in [17,18]. |
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