V. A. Abilov, F. V. Abilova, M. K. Kerimov, “On estimates for the Fourier-Bessel integral transform in the space <nobr>$L_2(\mathbb R_+)$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 7,Pages <nobr>1158

This article is cited in 7 papers

On estimates for the Fourier-Bessel integral transform in the space $L_2(\mathbb R_+)$

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. Kalinina 70, Makhachkala, 367015, Russia
^c Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: Two estimates useful in applications are proved for the Fourier–Bessel integral transform in$L_2(\mathbb R_+)$ as applied to some classes of functions characterized by a generalized modulus of continuity.

Key words: Fourier–Bessel integral transform, Bessel operator, generalized shift operator, generalized modulus of continuity, generalized derivatives, estimate.

UDC: 519.651

Received: 10.11.2008
Revised: 20.02.2009