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<p>We investigate uncertainty principles associated with the linear canonical Fourier–Bessel transform (LCFBT) and its wavelet counterpart. In the LCFBT setting, we establish a generalized Hardy-type theorem with polynomial weights, an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> </InlineEquation>–<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^q\)</EquationSource> </InlineEquation> version of Morgan’s theorem, and a Heisenberg–Weyl inequality with optimal constant obtained via a structural reduction to the classical Fourier–Bessel transform. We then extend the analysis to the linear canonical Fourier–Bessel wavelet transform (LCFBWT), deriving a Heisenberg-type inequality and an entropy-based uncertainty principle that provides a logarithmic lower bound for time–frequency–scale concentration. These results unify exponential, variance, and entropy uncertainty principles within the linear canonical Fourier–Bessel framework and clarify the role of the canonical parameters in localization phenomena.</p>

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On some uncertainty principles associated with the linear canonical Fourier–Bessel and linear canonical Fourier–Bessel wavelet transforms

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Fatima Elgadiri,
  • Hasnaa Lahmadi,
  • Abdellatif Akhlidj

摘要

We investigate uncertainty principles associated with the linear canonical Fourier–Bessel transform (LCFBT) and its wavelet counterpart. In the LCFBT setting, we establish a generalized Hardy-type theorem with polynomial weights, an \(L^p\) – \(L^q\) version of Morgan’s theorem, and a Heisenberg–Weyl inequality with optimal constant obtained via a structural reduction to the classical Fourier–Bessel transform. We then extend the analysis to the linear canonical Fourier–Bessel wavelet transform (LCFBWT), deriving a Heisenberg-type inequality and an entropy-based uncertainty principle that provides a logarithmic lower bound for time–frequency–scale concentration. These results unify exponential, variance, and entropy uncertainty principles within the linear canonical Fourier–Bessel framework and clarify the role of the canonical parameters in localization phenomena.