On invertibility of matrix wiener-hopf operator on discrete linearly ordered Abelian group

A connection between an invertibility of a matrix Wiener-Hopf operator on a discrete linearly ordered Abelian group and a canonical factoribility of the matrix symbol of the operator is studied. A method of the paper 1] is extended to the case of the group . Necessary and sufficient conditions for a normal solvability, a generalized invertibility, and an invertibility of the operator with a strictly nonsingular 2×2 matrix symbol of a special kind are found. We also give necessary conditions of the factoribility and necessary and sufficient conditions of the canonical factoribility of this matrix symbol.