Calderón’s type reproducing formula related to the \(q\)-Dunkl two wavelet theory. (English) Zbl 1540.44003
Summary: In this paper, using some elements of the \(q\)-harmonic analysis associated to the \(q\)-Dunkl operator introduced by N. Bettaibi and R. Bettaieb in [Tamsui Oxf. J. Math. Sci. 25, No. 2, 177–205 (2009; Zbl 1179.33020)], for fixed \(0< q <1\), the notion of a \(q\)-Dunkl two-wavelet is introduced. The resolution of the identity formula for the \(q\)-Dunkl continuous wavelet transform is then formulated and proved. Calderón’s type reproducing formula in the context of the \(q\)-Dunkl two wavelet theory is proved.
MSC:
| 44A05 | General integral transforms |
| 33B15 | Gamma, beta and polygamma functions |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
Citations:
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