Analogs of the Kolmogorov--Seliverstov--Plessner theorem for nonorthogonal function systems
Matematičeskie zametki, Tome 67 (2000) no. 1, pp. 87-101.

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

@article{MZM_2000_67_1_a9,
     author = {T. P. Lukashenko},
     title = {Analogs of the {Kolmogorov--Seliverstov--Plessner} theorem for nonorthogonal function systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {87--101},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_67_1_a9/}
}
TY  - JOUR
AU  - T. P. Lukashenko
TI  - Analogs of the Kolmogorov--Seliverstov--Plessner theorem for nonorthogonal function systems
JO  - Matematičeskie zametki
PY  - 2000
SP  - 87
EP  - 101
VL  - 67
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2000_67_1_a9/
LA  - ru
ID  - MZM_2000_67_1_a9
ER  - 
%0 Journal Article
%A T. P. Lukashenko
%T Analogs of the Kolmogorov--Seliverstov--Plessner theorem for nonorthogonal function systems
%J Matematičeskie zametki
%D 2000
%P 87-101
%V 67
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2000_67_1_a9/
%G ru
%F MZM_2000_67_1_a9
T. P. Lukashenko. Analogs of the Kolmogorov--Seliverstov--Plessner theorem for nonorthogonal function systems. Matematičeskie zametki, Tome 67 (2000) no. 1, pp. 87-101. http://geodesic.mathdoc.fr/item/MZM_2000_67_1_a9/

[1] Kolmogorov A. N., Seliverstov G. A., “Sur la convergence des séries de Fourier”, Compt. Rend. Acad. Sci. (Paris), 178 (1925), 303–305

[2] Kolmogorov A. N., Seliverstov G. A., “Sur la convergence des séries de Fourier”, Rend. R. Acad. Lincei., 3 (1926), 307–310

[3] Plessner A. I., “Über die Konvergenz von trigonometrischen Reihen”, J. Reine und Angew. Math., 155 (1926), 15–25

[4] Bari N. K., Trigonometricheskie ryady, GIFML, M., 1961

[5] Carleson L., “On convergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–157 | DOI | MR | Zbl

[6] Kaczmarz S., “Sur la convergence et la sommabilité des développements orthogonaux”, Studia Math., 1 (1929), 87–121

[7] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, GIFML, M., 1958

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

[9] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl

[10] Lukashenko T. P., “O sistemakh razlozheniya, podobnykh ortogonalnym”, Mezhdunarodn. konf. po teor. priblizh. funktsii, posv. pamyati prof. P. P. Korovkina, Tezisy dokl. T. 2 (Kaluga, 26–29 iyunya 1996 g.), Izd-vo TGU, Tver, 1996, 135–136

[11] Lukashenko T. P., “Sistemy razlozheniya, podobnye ortogonalnym”, Fundamentalnaya i prikladnaya matematika, 3:2 (1997), 487–517 | MR | Zbl

[12] Lukashenko T. P., “Ortopodobnye neotritsatelnye sistemy razlozheniya”, Vestn. MGU. Ser. I. Matem., mekh., 1997, no. 5, 27–31 | MR | Zbl

[13] Lukashenko T. P., “O koeffitsientakh sistem razlozheniya, podobnykh ortogonalnym”, Matem. sb., 188:12 (1997), 57–72 | MR | Zbl

[14] Lukashenko T. P., “Obobschennye sistemy razlozheniya, podobnye ortogonalnym”, Vestn. MGU. Ser. I. Matem., mekh., 1998, no. 4, 6–10 | MR | Zbl

[15] Lukashenko T. P., “O svoistvakh sistem razlozheniya, podobnykh ortogonalnym”, Izv. RAN. Ser. matem., 62:5 (1998), 187–206 | MR | Zbl

[16] Tandori K., “Weitere Bemerkungen über die Konvergenz und Summierbarkeit der Funktionenreihen”, Acta Math. Acad. Sci. Hung., 28:1–2 (1976), 119–127 | DOI | MR | Zbl

[17] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, T. 1, IL, M., 1962

[18] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, Izd. 7-oe, Nauka, M., 1970

[19] Kirillov A. A., Gvishiani A. D., Teoremy i zadachi funktsionalnogo analiza, Izd. 2-oe, Nauka, M., 1988