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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, the first aim of this article is to explore the main theorems of harmonic analysis of this novel transformation. The second aim is to study some quantitative uncertainty principles associated with the proposed transformation. Our third endeavour is to study the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1057_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> boundedness and compactness of localization operators associated with the DBWT. Further, we study their trace class properties and we prove that they are in the Schatten-von Neumann.</p>

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Dunkl-Bessel wavelet transform and localization operators

  • 期刊论文

  • 发表日期：

    2025年3月12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, the first aim of this article is to explore the main theorems of harmonic analysis of this novel transformation. The second aim is to study some quantitative uncertainty principles associated with the proposed transformation. Our third endeavour is to study the \(L^{p}\) L p boundedness and compactness of localization operators associated with the DBWT. Further, we study their trace class properties and we prove that they are in the Schatten-von Neumann.