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Trudy Moskovskogo Matematicheskogo Obshchestva
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Trudy Moskovskogo Matematicheskogo Obshchestva, 2015, Volume 76, Issue 1, Pages 67–84 (Mi mmo571)  
This article is cited in 9 scientific papers (total in 9 papers)

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

L. N. Lyakhov

Voronezh State University
Full-text PDF (304 kB) Citations (9)
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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.
Received: 31.03.2014
Revised: 02.06.2014
English version:
Transactions of the Moscow Mathematical Society, 2015, Volume 76, Issue 1, Pages 55–69
DOI: https://doi.org/10.1090/mosc/242
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 33C10, 42A38
Language: Russian
Citation: L. N. Lyakhov, “The construction of Dirichlet and de la Vallée–Poussin–Nikol'skiĭ kernels for j-Bessel Fourier integrals”, Tr. Mosk. Mat. Obs., 76, no. 1, MCCME, M., 2015, 67–84; Trans. Moscow Math. Soc., 76:1 (2015), 55–69
Citation in format AMSBIB
\Bibitem{Lya15}
\by L.~N.~Lyakhov
\paper The construction of Dirichlet and de la Vall\'ee--Poussin--Nikol'ski\u\i\ kernels for j-Bessel Fourier integrals
\serial Tr. Mosk. Mat. Obs.
\yr 2015
\vol 76
\issue 1
\pages 67--84
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo571}
\elib{https://elibrary.ru/item.asp?id=24850133}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2015
\vol 76
\issue 1
\pages 55--69
\crossref{https://doi.org/10.1090/mosc/242}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960089640}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Moskovskogo Matematicheskogo Obshchestva
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