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<p>Among the class of generalized Fourier transformations, the linear canonical transform is of pivotal importance mainly due to its higher degrees of freedom in lieu of the conventional Fourier and fractional Fourier transforms. This article is a continuation of the recent works on the linear canonical Dunkl transforms carried out in Ghazouani et al. (J Math Anal Appl 449:1797–1849, 2017), Mejjaoli (J Pseudo-Differ Oper Appl 16:1–43, 2025). Building upon this, we will introduce and study in this paper the generalized wavelet transform associated with the LCDT, called the Dunkl linear canonical wavelet transform. Then we will formulate several weighted uncertainty principles for this new transformation.</p>

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Dunkl linear canonical wavelet transform and applications

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Hatem Mejjaoli,
  • Sandeep Kumar Verma

摘要

Among the class of generalized Fourier transformations, the linear canonical transform is of pivotal importance mainly due to its higher degrees of freedom in lieu of the conventional Fourier and fractional Fourier transforms. This article is a continuation of the recent works on the linear canonical Dunkl transforms carried out in Ghazouani et al. (J Math Anal Appl 449:1797–1849, 2017), Mejjaoli (J Pseudo-Differ Oper Appl 16:1–43, 2025). Building upon this, we will introduce and study in this paper the generalized wavelet transform associated with the LCDT, called the Dunkl linear canonical wavelet transform. Then we will formulate several weighted uncertainty principles for this new transformation.