V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Some remarks concerning the Fourier transform in the space <nobr>$L_2(\mathbb R^n)$</nobr>”, Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 12,Pages <nobr>2113

This article is cited in 12 papers

Some remarks concerning the Fourier transform in the space $L_2(\mathbb R^n)$

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: For the Fourier transform in the space $L_2(\mathbb R^n)$ of square integrable multivariable functions, two practically useful estimates are proved in certain classes of functions characterized by a generalized continuity modulus.

Key words: integral Fourier transform, generalized derivatives, continuity modulus, estimates.

UDC: 519.651

Received: 23.07.2008