Abstract
A connection between an invertibility of a matrix Wiener-Hopf operator on a discrete linearly ordered Abelian group\(\mathbb{G}\) 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\(\mathbb{G}\). 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.
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Adukov, V. On invertibility of matrix wiener-hopf operator on discrete linearly ordered Abelian group. Integr equ oper theory 23, 373–386 (1995). https://doi.org/10.1007/BF01203913
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DOI: https://doi.org/10.1007/BF01203913