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<p>This paper establishes a harmonic analysis framework for the linear canonical Jacobi–Dunkl transform. We introduce three novel classes of wavelet packets and their associated transforms. For each, we prove Plancherel theorems and derive explicit reconstruction formulas, ensuring transform stability and invertibility. We also construct and characterize a set of novel scaling functions derived from the transform. The properties of these functions provide advanced tools for time–frequency analysis and pave the way for applications in mathematical physics and signal processing.</p>

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Linear canonical wavelet packets in the Jacobi–Dunkl setting

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Abdelaali Dades,
  • Othman Tyr,
  • Hatem Mejjaoli

摘要

This paper establishes a harmonic analysis framework for the linear canonical Jacobi–Dunkl transform. We introduce three novel classes of wavelet packets and their associated transforms. For each, we prove Plancherel theorems and derive explicit reconstruction formulas, ensuring transform stability and invertibility. We also construct and characterize a set of novel scaling functions derived from the transform. The properties of these functions provide advanced tools for time–frequency analysis and pave the way for applications in mathematical physics and signal processing.