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<p>The Dunkl-Bessel wavelet transform (DBWT) is a novel addition to the class of wavelet transforms. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, we investigate some problems of time-frequency analysis for this transform. In particular, we study the concept of the Dunkl-Bessel concentration operator and the scalogram analysis linked to the DBWT. We prove that a finite vector space generated by the first eigenfunctions of such operators has a maximal time-frequency concentration within the region of interest. Then, we will use it to approximate functions which are almost concentrated in such a region.</p>

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ACCUMULATED SCALOGRAM ASSOCIATED WITH THE DUNKL-BESSEL WAVELET TRANSFORM

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Hatem Mejjaoli,
  • Nadia Sraieb

摘要

The Dunkl-Bessel wavelet transform (DBWT) is a novel addition to the class of wavelet transforms. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, we investigate some problems of time-frequency analysis for this transform. In particular, we study the concept of the Dunkl-Bessel concentration operator and the scalogram analysis linked to the DBWT. We prove that a finite vector space generated by the first eigenfunctions of such operators has a maximal time-frequency concentration within the region of interest. Then, we will use it to approximate functions which are almost concentrated in such a region.