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Transactions of the Moscow Mathematical Society

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The construction of Dirichlet and de la Vallée-Poussin-Nikol'skiĭ kernels for $ \mathrm{j}$-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
DOI: https://doi.org/10.1090/mosc/242
Published electronically: November 17, 2015
MathSciNet review: 3467260
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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

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