Geodesic
A~method for constructing a~canonical matrix of solutions of a~Hilbert problem arising in the solution of convolution equations on~a~finite interval
Izvestiya. Mathematics , Tome 19 (1982) no. 3, pp. 559-610

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The Hilbert boundary value problem corresponding to a convolution equation on a finite interval, with kernel belonging to a class singled out earlier by the author, is reduced to a system of integral equations. The solvability of this system in appropriate weighted spaces is studied and an algorithm for constructing a canonical matrix of solutions of the Hilbert problem from certain solutions of the system. Estimates of partial indices are given. Bibliography: 15 titles. 
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     author = {B. V. Pal'tsev},
     title = {A~method for constructing a~canonical matrix of solutions of {a~Hilbert} problem arising in the solution of convolution equations on~a~finite interval},
     journal = {Izvestiya. Mathematics },
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B. V. Pal'tsev. A~method for constructing a~canonical matrix of solutions of a~Hilbert problem arising in the solution of convolution equations on~a~finite interval. Izvestiya. Mathematics , Tome 19 (1982) no. 3, pp. 559-610. http://geodesic.mathdoc.fr/item/IM2_1982_19_3_a4/