Geodesic
On some classes of Jacobi orthogonal series
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 121-132

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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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     author = {G. A. Fomin},
     title = {On some classes of {Jacobi} orthogonal series},
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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/