Geodesic
Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 939-945 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two useful estimates are proved for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus. 
@article{ZVMMF_2008_48_6_a0,
     author = {V. A. Abilov and F. V. Abilova and M. K. Kerimov},
     title = {Some remarks concerning the {Fourier} transform in the space $L_2(\mathbb R)$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {939--945},
     year = {2008},
     volume = {48},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a0/}
}
TY  - JOUR
AU  - V. A. Abilov
AU  - F. V. Abilova
AU  - M. K. Kerimov
TI  - Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 939
EP  - 945
VL  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a0/
LA  - ru
ID  - ZVMMF_2008_48_6_a0
ER  - 
%0 Journal Article
%A V. A. Abilov
%A F. V. Abilova
%A M. K. Kerimov
%T Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 939-945
%V 48
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a0/
%G ru
%F ZVMMF_2008_48_6_a0
V. A. Abilov; F. V. Abilova; M. K. Kerimov. Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 939-945. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a0/

[1] Titchmarsh E., Vvedenie v teoriyu integralov Fure, Izd. 2-e, Kom-Kniga, M., 2005

[2] Bokhner S., Lektsii ob integralakh Fure, Fizmatlit, M., 1962

[3] Dzhrbashyan M. M., Integralnoe preobrazovanie funktsii v kompleksnoi oblasti, Nauka, M., 1966

[4] Sveshnikov A. G., Bogolyubov A. N., Kravtsov V. V., Lektsii po matematicheskoi fizike, Nauka, M., 2004

[5] Zhukov A. I., Metod Fure v vychislitelnoi matematike, Fizmatlit, M., 1992 | MR | Zbl

[6] Plancherel M., “Contribution a l'etude de la representetion d'une fonction arbitraire par des integrales definies”, Rend. Circolo Matem. di Palermo, 30 (1910), 289–335 | DOI | Zbl

[7] Levi B., “Sul principio di Dirichlet”, Rend. Circolo Mat. di Palermo, 22 (1906), 293–359 | DOI

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

[9] Avilov V. A., Avilova F. V., “Nekotorye voprosy priblizheniya $2\pi$-periodicheskikh funktsii v prostranstve $L_2(2\pi)$”, Matem. zametki, 76:6 (2004), 803–811

[10] Zhidkov G. E., “Differentsialnye svoistva odnogo klassa funktsii”, Issl. po algebre i analizu, 1993, 42–46 | Zbl

[11] Kharishladze F. I., “Priblizhenie funktsii srednimi V. A. Steklova”, Tr. Tbilisskogo matem. in-ta AN Gruzii, 31, 1966, 55–70

[12] Kharshiladze F. I., “O funktsiyakh Steklova”, Soobsch. AN Gruz. SSR, 14:3 (1953), 139–144

[13] Panina E. G., “Nailuchshie priblizheniya funktsii i priblizheniya funktsiyami Steklova”, Vestn. MGU. Ser. 1. Matem. i mekhan., 2000, no. 2, 49–52

[14] Abilov V. A., “On the convergence of multiple Fourier series and quadrature formulae”, Math. Balcanica. New Series, 16:1–4 (2002), 73–94 | MR | Zbl