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

Author:
L. N. Lyakhov

Translated by:
E. Khukhro

Original publication:
Trudy Moskovskogo Matematicheskogo Obshchestva, tom **76** (2015), vypusk 1.

Journal:
Trans. Moscow Math. Soc. **2015**, 55-69

MSC (2010):
Primary 33C10; Secondary 42A38

Published electronically:
November 17, 2015

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**L. N. Lyakhov**

Affiliation:
Voronezh State University

Email:
levnlya@mail.ru

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

Keywords:
Generalized shift,
Bessel function,
even and odd Bessel j-functions,
Hankel (Bessel) transform,
Fourier--Bessel transform,
Dirichlet kernel,
de la Vall\'ee-Poussin kernel.

Published electronically:
November 17, 2015

Article copyright:
© Copyright 2015
L. N. Lyakhov