Conservative systems of integral convolution equations on the half-line and the entire line

The following system of integral convolution equations is considered: f(x) = g(x) + integral(a)(infinity) K(x-t)f(t) dt, -infinity less than or equal to a less than or equal to infinity, where the (m x m)-matrix-valued function K satisfies the conditions of conservativeness K-ij epsilon L-1 (R), K-ij greater than or equal to 0, A equivalent to integral(-infinity)(infinity) K(x) dx epsilon P-N, r(A) = 1. Here P-N is the class of non-negative indecomposable (m x m)-matrices and r(A) is the spectral radius of the matrix A. For a = 0 the equation in question is a conservative system of Wiener-Hopf integral equations. For a = -infinity this is the multidimensional renewal equation on the entire line. Questions of the solubility of the inhomogeneous and the homogeneous equations, asymptotic and other properties of solutions are considered: The method of non-linear factorization equations is applied and developed in combination with new results in multidimensional renewal theory.