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<p>We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley–Wiener theorem for the linear canonical Dunkl transform. Further, we characterize the square-integrable function <i>f</i> whose linear canonical Dunkl transform of the function is supported in the polynomial domain. Finally, we develop the Boas-type Paley–Wiener theorem for the linear canonical Dunkl transform.</p>

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Real Paley–Wiener theorems for the linear canonical Dunkl transform

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • S. Umamaheswari,
  • Sandeep Kumar Verma,
  • Hatem Mejjaoli

摘要

We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley–Wiener theorem for the linear canonical Dunkl transform. Further, we characterize the square-integrable function f whose linear canonical Dunkl transform of the function is supported in the polynomial domain. Finally, we develop the Boas-type Paley–Wiener theorem for the linear canonical Dunkl transform.