Geodesic
Nonsummability of almost everywhere orthorecursive expansions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 36-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It was proved earlier that only Weyl multiplier $\lambda_k$ with the property $\sum\limits_{k=1}^\infty \frac1{\lambda_k}<\infty$ provides the almost every where convergence of an orthorecurcive expansions of a function which does not converge to it in the norm. This result is extended to summation methods that sum a sequence being constant staring with some its element to its limit. 
@article{VMUMM_2024_3_a4,
     author = {A. A. Kiriukhina and T. P. Lukashenko},
     title = {Nonsummability of almost everywhere orthorecursive expansions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {36--39},
     year = {2024},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a4/}
}
TY  - JOUR
AU  - A. A. Kiriukhina
AU  - T. P. Lukashenko
TI  - Nonsummability of almost everywhere orthorecursive expansions
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2024
SP  - 36
EP  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a4/
LA  - ru
ID  - VMUMM_2024_3_a4
ER  - 
%0 Journal Article
%A A. A. Kiriukhina
%A T. P. Lukashenko
%T Nonsummability of almost everywhere orthorecursive expansions
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2024
%P 36-39
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a4/
%G ru
%F VMUMM_2024_3_a4
A. A. Kiriukhina; T. P. Lukashenko. Nonsummability of almost everywhere orthorecursive expansions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 36-39. http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a4/

[1] Lukashenko T.P., “Rekursivnye razlozheniya, podobnye ortogonalnym”, VII Mezhdunar. konf. “Matematika. Ekonomika. Ekologiya. Obrazovanie”. Mezhdunarodnyi simpozium “Ryady Fure i ikh prilozheniya”, Tez. dokl. (26 maya – 1 iyunya 1999 g.), RGEA, Rostov-na-Donu, 1999, 331

[2] Lukashenko T.P., “Ob ortorekursivnykh razlozheniyakh po kharakteristicheskim funktsiyam promezhutkov”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mat-ly shkoly-konf., posv. 130-letiyu so dnya rozhdeniya D.F. Egorova, Izd-vo “Kazan. mat. o-vo”, Kazan, 1999, 142–143

[3] Lukashenko T.P., “O svoistvakh ortorekursivnykh razlozhenii po neortogonalnym sistemam”, Vestn. Mosk. un-t. Matem. Mekhan., 2001, no. 1, 6–10 | Zbl

[4] Galatenko V.V., Lukashenko T.P., Sadovnichiy V.A., “Convergence almost everywhere of orthorecursive expansions in functional systems”, Advances in Dynamical Systems and Control, Studies in Systems, Decision and Control, 69, Springer Int. Publ. Switzerland, 2016, 3–11 ; Sadovnichii V.A., Izbrannye trudy. Matematika, mekhanika i ikh prilozheniya, v. 6, Izd-vo MGU, M., 2019, 200–207 | DOI | MR | Zbl

[5] Kashin B.S., Saakyan A.A., Ortogonalnye ryady, AFTs, M., 1999

[6] Aleksich G., Problemy skhodimosti ortogonalnykh ryadov, IL, M., 1963

[7] Bogachev V.I., Smolyanov O.G., Deistvitelnyi i funktsionalnyi analiz, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2009