Geodesic
Some estimates for the error in mixed Fourier–Bessel expansions of functions of two variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1545-1565 
V. A. Abilov; M. K. Kerimov. Some estimates for the error in mixed Fourier–Bessel expansions of functions of two variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1545-1565. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_9_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Some issues concerning expansions of functions of two variables in mixed Fourier–Bessel series are considered. In particular, the rate of their convergence in the classes of functions characterized by generalized moduli of continuity are estimated, and estimates of the remainder terms are obtained.

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR

[2] Abilov V. A., Kerimov M. K., “Ob otsenkakh ostatochnykh chlenov kratnykh ryadov Fure–Chebysheva i kubaturnykh formul chebyshevskogo tipa”, Zh. vychisl. matem. i matem. fiz., 43:5 (2003), 643–663 | MR | Zbl

[3] Abilov V. A., Abilov M. B., Kerimov M. K., “Nekotorye voprosy skhodimosti dvoinykh ryadov Fure–Lagerra–Ermita”, Zh. vychisl. matem. i matem. fiz., 44:12 (2004), 2128–2149 | MR | Zbl

[4] Vladimirov B. C., Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | MR | Zbl

[5] Kolmogorov A. N., Izbrannye trudy. Matematika i mekhanika, Nauka, M., 1987 | MR

[6] Abilov V. A., Abilova F. V., “Priblizhenie funktsii summami Fure–Besselya”, Izv. vuzov. Matematika, 2001, no. 8, 3–9 | MR | Zbl

[7] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR

[8] Bukhshtab A. A., Teoriya chisel, Prosveschenie, M., 1966 | Zbl

[9] Korneichuk H. P., Tochnye konstanty v teorii priblizhenii, Nauka, M., 1987