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<p>In this paper we examine the necessary and sufficient conditions on the sequences of some weighted norm of the Dunkl operators on functions in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1702_Article_IEq3.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{\kappa }^p(\mathbb {R}^d)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>κ</mi> </mrow> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> such that their support of the Dunkl transform is contained in a given compact set in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1702_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. As a corollary of the main result, a stronger version of real Paley-Wiener theorem for the Dunkl transform on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1702_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> is proved.</p>

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Sharper Paley-Wiener Theorem for the Dunkl Transform on \(\mathbb {R}^d\)

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Minggang Fei,
  • Dongyan Zhang,
  • Jiali Zhou

摘要

In this paper we examine the necessary and sufficient conditions on the sequences of some weighted norm of the Dunkl operators on functions in \(L_{\kappa }^p(\mathbb {R}^d)\) L κ p ( R d ) such that their support of the Dunkl transform is contained in a given compact set in \(\mathbb {R}^d\) R d . As a corollary of the main result, a stronger version of real Paley-Wiener theorem for the Dunkl transform on \(\mathbb {R}^d\) R d is proved.