We characterize left, right and both-sided invertibility of matrix Wiener--Hopf plus Hankel operators with possibly different Fourier symbols in the Wiener subclass of the almost periodic algebra. This is done when a certain almost periodic matrix-valued function (constructed from the initial Fourier symbols of the Hankel and Wiener–Hopf operators) admits a numerical range bounded away from zero. The invertibility characterization is based on the value of a certain mean motion. At the end, an example of a concrete Wiener–Hopf plus Hankel operator is studied in view of the illustration of the proposed theory.
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L. P. Castro, A. S. Silva, Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range. Z. Anal. Anwend. 28 (2009), no. 1, pp. 119–127DOI 10.4171/ZAA/1376