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Factorization theory for Wiener–Hopf plus Hankel operators with almost periodic symbols. (English) Zbl 1118.47021

Han, Deguang (ed.) et al., Operator theory, operator algebras, and applications. Proceedings of the 25th Great Plains Operator Theory Symposium, University of Central Florida, FL, USA, June 7–12, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3923-3/pbk). Contemporary Mathematics 414, 111-128 (2006).
The theory of Wiener–Hopf plus Hankel operators is well developed for some classes of Fourier symbols. In particular, the invertibility and Fredholm properties of such kind of operators are known. The aim of this paper is the characterization of the invertibility and Fredholm properties of Wiener–Hopf plus Hankel operators with almost periodic Fourier symbols. To do this, several useful details about almost periodic functions, operator identities for Wiener-Hopf plus Hankel operators and factorization concepts are recalled. Also, a new kind of almost periodic factorization, the so-called almost periodic asymmetric factorization, is analysed. As a consequence of the main result, a dependence between the invertibility of Wiener–Hopf and Wiener–Hopf plus Hankel operators with the same almost periodic Fourier symbol is obtained.
For the entire collection see [Zbl 1100.47500].

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47A53 (Semi-) Fredholm operators; index theories
42A75 Classical almost periodic functions, mean periodic functions
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