Abstract:
Systems of $n$ convolution equations of the first and second kind on a finite interval are reduced to a Riemann boundary value problem for a vector function of length $2n$. We prove a theorem about the equivalence of the Riemann problem and the initial system. Sufficient conditions are obtained for the well-posedness of a system of the second kind. Also under study is the case of the periodic kernel of the integral operator of a system of the first and second kind.
Keywords:system of convolution equations, finite interval, factorization, Riemann boundary value problem, partial indices.
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