Geodesic
Estimates for the Fourier–Bessel transforms of multivariate functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 980-989 
V. A. Abilov; M. K. Kerimov. Estimates for the Fourier–Bessel transforms of multivariate functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 6, pp. 980-989. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_6_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two estimates useful in applications are proved for the Fourier–Bessel (or Hankel) transform in the space for some classes of two-variable functions characterized by a generalized modulus of continuity.

[1] Dzharbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[2] Bokhner S., Lektsiya v integralakh Fure, Fizmatgiz, M., 1962

[3] Kipriyanov I. A., “Preobrazovaniya Fure–Besselya i teoremy vlozheniya dlya vesovykh klassov”, Tr. matem. inst. AN SSSR, 79, Nauka, M., 1966, 130–213

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

[5] Levitan B. M., “Razlozheniya po funktsiyam Besselya v ryady i integraly Fure”, Uspekhi matem. nauk, 6:2 (1951), 102–143 | MR | Zbl

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

[7] Abilov V. A., Abilova F. V., “Nekotorye voprosy skhodimosti kratnykh ryadov Fure”, Zh. vychisl. matem. i matem. fiz., 39:12 (1999), 1951–1961 | MR | Zbl

[8] Abilov V. A., Abilova F. V., Kerimov M. K., “O nekotorykh otsenkakh dlya integralnogo preobrazovaniya Fure–Besselya v prostranstve $\mathbb{L}_2(\mathbb{R}_+)$”, Zh. vychisl. matem. i matem. fiz., 49:7 (2009), 1158–1166 | MR | Zbl

[9] Abilov V. A., Abilova F. V., Kerimov M. K., “Nekotorye voprosy razlozheniya funktsii v dvoinye ryady Fure–Besselya”, Zh. vychisl. matem. i matem. fiz., 44:12 (2004), 2128–2149 | MR | Zbl

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

[11] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | Zbl