This article is cited in 2 papers

A method for constructing a canonical matrix of solutions of a Hilbert problem arising in the solution of convolution equations on a finite interval

B. V. Pal'tsev


Abstract: 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.

UDC: 517.968.72+53

MSC: Primary 30E25, 45B05, 45E10; Secondary 35Q15, 45E05, 45F05, 44A15, 46E30, 47A53

Received: 29.05.1981

 English version: Mathematics of the USSR-Izvestiya, 1982, 19:3, 559–610

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