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Calderón’s reproducing formula and uncertainty principle for the continuous wavelet transform associated with the q-Bessel operator

  • Bochra Nefzi
  • Kamel Brahim
Article

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.

Keywords

q-Wavelet Continuous q-wavelet transform q-Bessel operator q-Bessel Fourier transform Calderón’s reproducing formula Uncertainty principle Heisenberg–Pauli–Weyl inequality 

Mathematics Subject Classification

33B15 33D05 44A20 42A38 42B10 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Faculty of Sciences of TunisUniversity of Tunis El ManarTunisTunisia

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