Systems of convolution equations of the first and second kind on a finite interval and factorization of matrix-functions

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.