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<p>We ask to what extent the Bessel function of the first kind involved in the definition of the Fourier-Bessel transforms, both continuous and discrete, can be replaced by the Bessel function of the second kind to keep their basic properties, e.g. Plancherel’s or Parseval’s identity, respectively. The answer we provide in this note is somehow surprising.</p>

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Fourier-Bessel Transforms Based on Bessel Functions of the Second Kind

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Krzysztof Stempak

摘要

We ask to what extent the Bessel function of the first kind involved in the definition of the Fourier-Bessel transforms, both continuous and discrete, can be replaced by the Bessel function of the second kind to keep their basic properties, e.g. Plancherel’s or Parseval’s identity, respectively. The answer we provide in this note is somehow surprising.