Geodesic
Expansion in eigenfunctions of integral operators of convolution on a~finite interval with kernels whose Fourier transforms are rational. ``Weakly'' nonselfadjoint regular kernels
Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 587-630

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A study is made of the asymptotic behavior of the eigenvalues and of expansions in the root vectors of the class of integral operators specified in the title. If some natural conditions, ensuring “regularity” of the asymptotic behavior of the spectrum, are imposed on the kernel, the root vectors form a basis in $L_p(0,T)$ $(1$ and a Riesz basis in $L_2(0,T)$. 
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     author = {B. V. Pal'tsev},
     title = {Expansion in eigenfunctions of integral operators of convolution on a~finite interval with kernels whose {Fourier} transforms are rational. {``Weakly''} nonselfadjoint regular kernels},
     journal = {Izvestiya. Mathematics },
     pages = {587--630},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a9/}
}
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B. V. Pal'tsev. Expansion in eigenfunctions of integral operators of convolution on a~finite interval with kernels whose Fourier transforms are rational. ``Weakly'' nonselfadjoint regular kernels. Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 587-630. http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a9/