Geodesic
The construction of Dirichlet and de la Vall\'ee--Poussin--Nikol'ski\u\i\ kernels for j-Bessel Fourier integrals
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 76 (2015) no. 1, pp. 67-84

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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. 
@article{MMO_2015_76_1_a1,
     author = {L. N. Lyakhov},
     title = {The construction of {Dirichlet} and de la {Vall\'ee--Poussin--Nikol'ski\u\i\} kernels for {j-Bessel} {Fourier} integrals},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {67--84},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a1/}
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L. N. Lyakhov. The construction of Dirichlet and de la Vall\'ee--Poussin--Nikol'ski\u\i\ kernels for j-Bessel Fourier integrals. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 76 (2015) no. 1, pp. 67-84. http://geodesic.mathdoc.fr/item/MMO_2015_76_1_a1/