Theoretical analysis establishes the extension of canonical Fourier–Bessel operators to generalized distributions, providing foundational analogues of classical Paley–Wiener theorems.
We study some problems of the canonical Fourier–Bessel harmonic analysis of distributions. Basic concepts of the canonical Fourier–Bessel harmonic analysis are expanded to distributions, among them the canonical Fourier–Bessel transform, the generalized translation operator associated with the canonical Bessel differential operator and others. The analogues of various results of classical harmonic analysis, including analogues of the Paley–Wiener theorems, are proved.
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С. С. Платонов (2026) studied this question.
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