V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Sharp estimates for the convergence rate of Fourier–Bessel series”, Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 6,Pages <nobr>917

This article is cited in 7 papers

Sharp estimates for the convergence rate of Fourier–Bessel series

V. A. Abilov^a, F. V. Abilova^b, M. K. Kerimov^c

^a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
^b Dagestan State Technical University, pr. Shamilya 70, Makhachkala, 367015, Russia
^c Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Sharp estimates are derived for the convergence rate of Fourier series in terms of Bessel functions of the first kind for some classes of functions characterized by a generalized modulus of continuity. The Kolmogorov $N$-width of these classes of functions are also estimated.

Key words: Bessel functions, Fourier–Bessel series, generalized modulus of continuity, Kolmogorov $N$-width, sharp estimates for convergence rates of series.

UDC: 519.651

Received: 21.01.2015

DOI: 10.7868/S0044466915060022