This article is cited in 10 papers

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

L. N. Lyakhov

Voronezh State University

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.

Key words and phrases: Generalized shift, Bessel function, even and odd Bessel j-functions, Hankel (Bessel) transform, Fourier–Bessel transform, Dirichlet kernel, de la Vallée-Poussin kernel.

UDC: 517.9

MSC: 33C10, 42A38

Received: 31.03.2014
Revised: 02.06.2014

 English version: Transactions of the Moscow Mathematical Society, 2015, 76:1, 55–69

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