Abstract
In this paper, we present some new elements of harmonic analysis related to the q-Bessel Fourier transform introduced earlier in Dhaouadi (Bull Math Anal Appl 5(2):42–60, 2013), Dhaouadi et al. (J Inequal Pure Appl Math 7(5):171, 2006), we define and study the q-wavelet and the continuous q-wavelet transform associated with this harmonic analysis. Thus, some results (Plancherel’s formula, inversion formula, etc.) are established. Next, we prove a Calderón’s formula and an analogue of Heisenberg’s inequality for the continuous q-wavelet transform.
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Nefzi, B., Brahim, K. Calderón’s reproducing formula and uncertainty principle for the continuous wavelet transform associated with the q-Bessel operator. J. Pseudo-Differ. Oper. Appl. 9, 495–522 (2018). https://doi.org/10.1007/s11868-017-0209-9
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DOI: https://doi.org/10.1007/s11868-017-0209-9
Keywords
- q-Wavelet
- Continuous q-wavelet transform
- q-Bessel operator
- q-Bessel Fourier transform
- Calderón’s reproducing formula
- Uncertainty principle
- Heisenberg–Pauli–Weyl inequality