The construction of Dirichlet and de la Vallée-Poussin–Nikol’skiĭ kernels for 𝑗-Bessel Fourier integrals

Lyakhov, L.

doi:10.1090/mosc/242

The construction of Dirichlet and de la Vallée-Poussin–Nikol’skiĭ kernels for $\mathrm {j}$-Bessel Fourier integrals
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by L. N. Lyakhov
Translated by: E. Khukhro

Trans. Moscow Math. Soc. 2015, 55-69

DOI: https://doi.org/10.1090/mosc/242

Published electronically: November 17, 2015

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Abstract:

We give elementary proofs of some properties of the generalized shift generated by a spherical symmetry. We construct B-kernels for Fourier integrals with respect to Bessel j-functions (Fourier–Bessel transforms). These are designed to play the same role as Dirichlet and de la Vallée-Poussin–Nikol’skiĭ kernels in the theory of trigonometric Fourier integrals and in the theory of function approximation.

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