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<p>In this paper, we introduce the notion of the Wigner distribution in the Dunkl type operator setting. We examine the underlying theory of localization operators. Particularly, we study the trace class properties of such operators and also demonstrate that they belong to the Schatten-von Neumann class. Nonetheless, special attention is paid to the boundedness and compactness of the localization operators associated with the generalized Wigner distribution on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1744_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}_{A}(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mi>A</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1744_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(1 \le p \le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> in the typical cases: the Dunkl Wigner distribution, the Jacobi-Dunkl Wigner distribution and the Wigner distribution in the Chébli-Trimèche hypergroup.</p>

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Generalized Wigner Distribution Associated with the Dunkl Type Operator and Localization Operators

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Saifallah Ghobber,
  • Hatem Mejjaoli

摘要

In this paper, we introduce the notion of the Wigner distribution in the Dunkl type operator setting. We examine the underlying theory of localization operators. Particularly, we study the trace class properties of such operators and also demonstrate that they belong to the Schatten-von Neumann class. Nonetheless, special attention is paid to the boundedness and compactness of the localization operators associated with the generalized Wigner distribution on \(L^{p}_{A}(\mathbb {R})\) L A p ( R ) , \(1 \le p \le \infty \) 1 ≤ p ≤ ∞ in the typical cases: the Dunkl Wigner distribution, the Jacobi-Dunkl Wigner distribution and the Wigner distribution in the Chébli-Trimèche hypergroup.