Geodesic
On some classes of Jacobi orthogonal series
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 121-132 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions are given which can be imposed on the coefficients of an orthogonal series of Jacobi polynomials and which, when fulfilled, guarantee that the series is a Fourier–Jacobi series; and the question of its convergence in mean is solved. The results are analogues of known theorems for cosine-series due to Kolmogorov, Szidon, Telyakovskii and the author. Bibliography: 9 titles. 
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G. A. Fomin. On some classes of Jacobi orthogonal series. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 121-132. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a7/

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[2] Kolmogorov A. N., “Sur l'ordre de grandeur des coefficients de la serie de Fourier – Le besgue”, Bull, polon. Sci. (A), 1923, 83–86

[3] Telyakovskii S. A., “Ob odnom dostatochnom uslovii Sidona integriruemosti trigonometricheskikh ryadov”, Matem. zametki, 14:3 (1973), 317–328

[4] Sidon S., “Hinreichende Bedingungen für den Fourier – Charakter einer trigonometrischen Reihe”, J. London Math. Soc., 14:2 (1939), 158–160 | DOI | Zbl

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