Geodesic
An Example of the Sequence of Coefficients of a Double Trigonometric Series
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 45-52

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

We construct an example of a double sequence $a$ of nonnegative numbers that are monotone decreasing to zero in the first index for any fixed value of the second index and two Hadamard lacunary sequences of natural numbers such that the double trigonometric lacunary monotone series with the coefficients $a$ constructed from the first lacunary sequence is square-divergent almost everywhere and the one constructed from the second lacunary sequence is square-convergent almost everywhere.
Keywords: double trigonometric series, Hadamard lacunary sequence, square-convergent series, lacunary monotone coefficient, Pringsheim convergence, Fourier series. 
M. I. Dyachenko. An Example of the Sequence of Coefficients of a Double Trigonometric Series. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 45-52. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/
@article{MZM_2011_90_1_a5,
     author = {M. I. Dyachenko},
     title = {An {Example} of the {Sequence} of {Coefficients} of a {Double} {Trigonometric} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {45--52},
     year = {2011},
     volume = {90},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/}
}
TY  - JOUR
AU  - M. I. Dyachenko
TI  - An Example of the Sequence of Coefficients of a Double Trigonometric Series
JO  - Matematičeskie zametki
PY  - 2011
SP  - 45
EP  - 52
VL  - 90
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/
LA  - ru
ID  - MZM_2011_90_1_a5
ER  - 
%0 Journal Article
%A M. I. Dyachenko
%T An Example of the Sequence of Coefficients of a Double Trigonometric Series
%J Matematičeskie zametki
%D 2011
%P 45-52
%V 90
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a5/
%G ru
%F MZM_2011_90_1_a5

[1] M. I. Dyachenko, S. Yu. Tikhonov, “Dvoinye trigonometricheskie ryady s lakunarno-monotonnymi koeffitsientami”, Materialy Mezhdunarodnoi nauchnoi konferentsii “Sovremennye problemy matematiki, mekhaniki, informatiki”, Tula, 2009, 37–39

[2] M. I. Dyachenko, S. Yu. Tikhonov, “Gladkost dvoinykh trigonometricheskikh ryadov s lakunarno-monotonnymi koeffitsientami”, Tezisy dokladov 15-i Saratovskoi zimnei shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya”, Saratov, 2010, 72–73

[3] A. S. Belov, “O nulyakh summy trigonometricheskogo ryada s monotonnymi koeffitsientami”, Izv. vuzov. Matem., 1989, no. 12, 3–8 | MR | Zbl

[4] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR