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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 1, 2009, pp. 119–127
DOI: 10.4171/ZAA/1376

Published online: 2009-03-31

Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range

L. P. Castro[1] and A. S. Silva[2]

(1) Universidade de Aveiro, Portugal
(2) Universidade de Aveiro, Portugal

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.

Keywords: Wiener–Hopf operator, Hankel operator, almost periodic function, invertibility

Castro L. P., Silva A. S.: Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range. Z. Anal. Anwend. 28 (2009), 119-127. doi: 10.4171/ZAA/1376