Geodesic
Equiconvergence theorem for expansions in eigenfunctions of integral operators with discontinuous involution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 5-10.

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In the paper we consider the equiconvergence of expansions in trigonometric Fourier series and in eigen- and associated functions of integral operators with involution having discontinuities of the first type. 
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A. V. Golub; A. P. Khromov. Equiconvergence theorem for expansions in eigenfunctions of integral operators with discontinuous involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 5-10. http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a1/

[1] Khromov A. P., “Integralnye operatory s yadrami, razryvnymi na lomanykh liniyakh”, Mat. sb., 197:11 (2006), 115–142 | DOI | MR | Zbl

[2] Kornev V. V., Khromov A. P., “O ravnoskhodimosti razlozhenii po sobstvennym funktsiyam integralnykh operatorov s yadrami, dopuskayuschimi razryvy proizvodnykh na diagonalyakh”, Mat. sb., 192:10 (2001), 33–50 | DOI | MR | Zbl