Geodesic
Riesz bases of eigenfunctions of integral operators with kernels discontinuous on the diagonals
Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1175-1189.

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We prove the Riesz basis property in $L_2[0,1]$ for the family of eigenfunctions and adjoint functions of an integral operator whose kernel is discontinuous on the diagonals $t=x$ and $t=1-x$.
Keywords: Riesz basis, resolvent, characteristic number, eigenfunction, involution. 
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V. P. Kurdyumov; A. P. Khromov. Riesz bases of eigenfunctions of integral operators with kernels discontinuous on the diagonals. Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1175-1189. http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a6/

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