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 
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/
@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

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

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.

[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