THE CONSTRUCTION OF DIRICHLET AND DE LA VALL′EE-POUSSIN–NIKOL’SKI? KERNELS FOR j-BESSEL FOURIER INTEGRALS

摘要

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’ski? kernels in the theory of trigonometric Fourier integrals and in the theory of function approximation.