Geodesic
Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals
Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1451-1469 
V. V. Kornev; A. P. Khromov. Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals. Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1451-1469. http://geodesic.mathdoc.fr/item/SM_2001_192_10_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Simple conditions are found ensuring the equiconvergence of the Fourier expansion of a function $f(x)$ in $L[0,1]$ in the eigenfunctions and the associated functions of an integral operator $$ Af=\int_0^{1-x}A(1-x,t)f(t)\,dt+\alpha\int_0^xA(x,t)f(t)\,dt $$ and the expansions of $f(x)$ and $f(1-x)$ in the standard trigonometric system.

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