Geodesic
Riescz Basis Property of Eigen and Associated Functions of Integral Operators with Discontinuous Kernels, Containing Involution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 558-569 
V. P. Kurdumov; A. P. Khromov. Riescz Basis Property of Eigen and Associated Functions of Integral Operators with Discontinuous Kernels, Containing Involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 558-569. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a9/
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     title = {Riescz {Basis} {Property} of {Eigen} and {Associated} {Functions} of {Integral} {Operators} with {Discontinuous} {Kernels,} {Containing} {Involution}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For invertible integral operator which kernel is discontinuous on the diagonals of the unit square Riescz basis property of its eigen and associated functions in $L_2[0,1]$ is proved.

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