JournalszaaVol. 28, No. 1pp. 119–127

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

  • L. P. Castro

    Universidade de Aveiro, Portugal
  • A. S. Silva

    Universidade de Aveiro, Portugal
Invertibility of Matrix Wiener–Hopf plus Hankel Operators with Symbols Producing a Positive Numerical Range cover
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Abstract

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.

Cite this article

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. 119–127

DOI 10.4171/ZAA/1376