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

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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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     author = {V. P. Kurdumov and A. P. Khromov},
     title = {Riescz {Basis} {Property} of {Eigen} and {Associated} {Functions} of {Integral} {Operators} with {Discontinuous} {Kernels,} {Containing} {Involution}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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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/