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<p>We introduce wavelet transforms associated with the Hartley-Bessel transform and develop their fundamental theory. The continuous Hartley-Bessel wavelet transform is defined along with its existence and reconstruction formulas, and its Plancherel-Parseval relations are established. New bounds for the Hartley-Bessel translation operator are established. These results are a continuation of Tuan’s approach <a href="https://arxiv.org/abs/2508.02787v1">https://arxiv.org/abs/2508.02787v1</a>, where he studied a new upper bound coefficient of the structure convolution which is first studied by Bouzeffour (J. Pseudo-Differ. Oper. Appl. <CitationRef CitationID="CR5">2024</CitationRef> 15:42). As applications, we derive Abel-Tauber-type theorems and uncertainty principle inequalities for CH-BWT.</p>

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ANALYSIS OF WAVELET TRANSFORMS ARISING FROM THE HARTLEY-BESSEL TRANSFORM

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Mohamed Amine Boubatra

摘要

We introduce wavelet transforms associated with the Hartley-Bessel transform and develop their fundamental theory. The continuous Hartley-Bessel wavelet transform is defined along with its existence and reconstruction formulas, and its Plancherel-Parseval relations are established. New bounds for the Hartley-Bessel translation operator are established. These results are a continuation of Tuan’s approach https://arxiv.org/abs/2508.02787v1, where he studied a new upper bound coefficient of the structure convolution which is first studied by Bouzeffour (J. Pseudo-Differ. Oper. Appl. 2024 15:42). As applications, we derive Abel-Tauber-type theorems and uncertainty principle inequalities for CH-BWT.