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On the Fredholm property and index of Wiener-Hopf plus/minus Hankel operators with piecewise almost periodic symbols. (English) Zbl 1187.47022

Summary: The characterization of a Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with piecewise almost periodic Fourier symbols is obtained. The conditions that ensure the Fredholm property are mainly based on the factorization of certain almost periodic matrix functions, and spectral properties of some others. In addition, Fredholm index formulas are also obtained based on an extension of the Cauchy index notion which is therefore applied to some new functions derived from the symbols of the operators.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A53 (Semi-) Fredholm operators; index theories
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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