Geodesic
On sharp estimates of the convergence of double Fourier–Bessel series
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1765-1770

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The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier–Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented. 
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     author = {V. A. Abilov and F. V. Abilova and M. K. Kerimov},
     title = {On sharp estimates of the convergence of double {Fourier{\textendash}Bessel} series},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1765--1770},
     publisher = {mathdoc},
     volume = {57},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a0/}
}
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V. A. Abilov; F. V. Abilova; M. K. Kerimov. On sharp estimates of the convergence of double Fourier–Bessel series. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1765-1770. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a0/