Some inverse theorems for approximation of functions by Fourier--Laguerre sums
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 3-9.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove two inverse theorems of the approximation of functions of two variables by Fourier–Laguerre sums in a space with a certain weight.
Mots-clés : Fourier–Laguerre transform
Keywords: generalized shift operator, generalized derivatives.
@article{IVM_2010_9_a0,
     author = {V. A. Abilov and F. V. Abilova and M. V. Abilov},
     title = {Some inverse theorems for approximation of functions by {Fourier--Laguerre} sums},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {9},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_9_a0/}
}
TY  - JOUR
AU  - V. A. Abilov
AU  - F. V. Abilova
AU  - M. V. Abilov
TI  - Some inverse theorems for approximation of functions by Fourier--Laguerre sums
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 3
EP  - 9
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_9_a0/
LA  - ru
ID  - IVM_2010_9_a0
ER  - 
%0 Journal Article
%A V. A. Abilov
%A F. V. Abilova
%A M. V. Abilov
%T Some inverse theorems for approximation of functions by Fourier--Laguerre sums
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 3-9
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_9_a0/
%G ru
%F IVM_2010_9_a0
V. A. Abilov; F. V. Abilova; M. V. Abilov. Some inverse theorems for approximation of functions by Fourier--Laguerre sums. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2010_9_a0/

[1] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[2] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[3] Abilov V. A., “On the best approximation of functions of many variables by algebraic polynomials”, East J. Approx., 2:4 (1996), 477–497 | MR | Zbl

[4] Rzhavinskaya E. V., “O priblizhenii funktsii v srednem summami Fure–Lagerra”, Izv. vuzov. Matematika, 1979, no. 11, 87–93 | MR | Zbl

[5] Abilov V. A., “Priblizhenie funktsii summami Fure–Lagerra”, Matem. zametki, 57:2 (1995), 163–170 | MR | Zbl

[6] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960