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<p>In this paper, we introduce the notion of linear canonical Dunkl Wigner transformation and 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 linear canonical Dunkl Wigner transformation on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2025_719_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}_{k}(\mathbb {R}^{N})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mi>k</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2025_719_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>.</p>

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Linear canonical Dunkl Wigner transformation: theory and localization operators

  • 期刊论文

  • 发表日期：

    2025年8月2日

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  • Hatem Mejjaoli

摘要

In this paper, we introduce the notion of linear canonical Dunkl Wigner transformation and 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 linear canonical Dunkl Wigner transformation on \(L^{p}_{k}(\mathbb {R}^{N})\) L k p ( R N ) , \(1 \le p \le \infty \) 1 ≤ p ≤ ∞ .