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<p>The purpose of this paper is to verify a novel uncertainty principle regarding the Jacobi-Dunkl transform. This discovery expands upon the Donoho-Stark result, indicating that it is impossible for both a non-zero function <i>f</i> and its Jacobi-Dunkl transform <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40863_2024_488_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {F}}_{\alpha ,\beta }(f)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">F</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> to have finite measures of support. Furthermore, we extend the signal recovery problem to encompass the Jacobi-Dunkl transform.</p>

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\(L^p\)-Donoho-Stark principle for Jacobi-Dunkl transform

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Najat Safouane,
  • Azzedine Achak,
  • El Mehdi Loualid

摘要

The purpose of this paper is to verify a novel uncertainty principle regarding the Jacobi-Dunkl transform. This discovery expands upon the Donoho-Stark result, indicating that it is impossible for both a non-zero function f and its Jacobi-Dunkl transform \({\mathcal {F}}_{\alpha ,\beta }(f)\) F α , β ( f ) to have finite measures of support. Furthermore, we extend the signal recovery problem to encompass the Jacobi-Dunkl transform.