Geodesic
Orthonormal bases of multidimensional trigonometric polynomials, consisting of translations of one of them
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2020), pp. 48-52 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Orthonormal bases of consecutive shifts of one polynomial are constructed in some spaces of multidimensional trigonometric polynomials. The methods for constructing Parseval frames of consecutive shifts of a polynomial in wider classes of multidimensional trigonometric polynomials are proposed. 
@article{VMUMM_2020_3_a7,
     author = {T. P. Lukashenko},
     title = {Orthonormal bases of multidimensional trigonometric polynomials, consisting of translations of one of them},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {48--52},
     year = {2020},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a7/}
}
TY  - JOUR
AU  - T. P. Lukashenko
TI  - Orthonormal bases of multidimensional trigonometric polynomials, consisting of translations of one of them
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2020
SP  - 48
EP  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a7/
LA  - ru
ID  - VMUMM_2020_3_a7
ER  - 
%0 Journal Article
%A T. P. Lukashenko
%T Orthonormal bases of multidimensional trigonometric polynomials, consisting of translations of one of them
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2020
%P 48-52
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a7/
%G ru
%F VMUMM_2020_3_a7
T. P. Lukashenko. Orthonormal bases of multidimensional trigonometric polynomials, consisting of translations of one of them. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2020), pp. 48-52. http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a7/

[1] Lukashenko T. P., “Bazisy trigonometricheskikh mnogochlenov iz sdvigov yader Dirikhle”, Vestn. Mosk. un-ta. Matem. Mekhan., 2014, no. 5, 35–40 | Zbl

[2] Lukashenko T. P., “Ortogonalnye bazisy sdvigov v prostranstvakh trigonometricheskikh mnogochlenov”, Izv. Saratov. un-ta. Nov. ser. Ser. Matem. Mekhan. Inform., 14:4-1 (2014), 367–373 | Zbl

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2004

[4] Bogachev V. I., Smolyanov O. G., Deistvitelnyi i funktsionalnyi analiz: Universitetskii kurs, NITs RKhD, M.–Izhevsk, 2009; 2011

[5] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2005 | MR

[6] Fadeeva A. V., “Freimy Parsevalya iz posledovatelnykh sdvigov odnoi funktsii v prostranstvakh trigonometricheskikh mnogochlenov”, Vestn. Mosk. un-ta. Matem. Mekhan., 2018, no. 6, 30–36 | Zbl