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<p>This research paper explores Parseval-Goldstein type relations associated with the Dunkl transform on <InlineEquation ID="IEq1"> <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> for a Coxeter group <i>G</i>. It investigates the properties of the Dunkl transform and its adjoint over Lebesgue spaces. An application to the Dunkl transform on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(G=\mathbb {Z}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> is discussed. The results of this paper are illustrated by some examples.</p>

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Parseval-Goldstein type theorems for the Dunkl transform

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Fethi Soltani,
  • Kais Ammari

摘要

This research paper explores Parseval-Goldstein type relations associated with the Dunkl transform on \(\mathbb {R}^d\) R d for a Coxeter group G. It investigates the properties of the Dunkl transform and its adjoint over Lebesgue spaces. An application to the Dunkl transform on \(\mathbb {R}\) R for \(G=\mathbb {Z}_2\) G = Z 2 is discussed. The results of this paper are illustrated by some examples.