Geodesic
A Condition for Convergence in Mean of Trigonometric Series
Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 323-328 
A. S. Belov. A Condition for Convergence in Mean of Trigonometric Series. Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 323-328. http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a0/
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     author = {A. S. Belov},
     title = {A {Condition} for {Convergence} in {Mean} of {Trigonometric} {Series}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We construct an example of a trigonometric series showing that a certain condition closely related to convergence in mean of trigonometric series cannot be sharpened.

[1] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961

[2] Belov A. S., Izv. Tulskogo gos. un-ta. Ser. Matem. Mekh. Informatika, 4:1 (1998), 40–46 | MR

[3] Fomin G. A., “Über die Konvergenz im Mittel von Fourierreihen”, Matem. sb., 110:2 (1979), 251–265 | MR | Zbl

[4] Rudin W., “Some theorems on Fourier coefficients”, Proc. Amer. Math. Soc., 10:4 (1959), 855–859 | DOI | MR | Zbl

[5] Brillhart J., Carlitz L., “Note on the Shapiro polynomials”, Proc. Amer. Math. Soc., 25:1 (1970), 114–118 | DOI | MR | Zbl

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