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

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 Vall´ee-Poussin–Nikol’ski˘ı kernels in the theory of trigonometric Fourier integrals and in the theory of function approximation.