Luís P. Castro and Anabela S. Silva

Wiener-Hopf and Wiener-Hopf-Hankel Operators with Piecewise-Almost Periodic Symbols on Weighted Lebesgue Spaces

abstract:
We consider Wiener-Hopf, Wiener-Hopf plus Hankel, and Wiener-Hopf minus Hankel operators on weighted Lebesgue spaces and having piecewise almost periodic Fourier symbols. The main results concern conditions to ensure the Fredholm property and the lateral invertibility of these operators. In addition, under the Fredholm property, conclusions about the Fredholm index of those operators are also discussed.

Mathematics Subject Classification: 47B35, 42A75, 47A53, 47A68, 47G10

Key words and phrases: Wiene-Hopf operator, Hankel operator, Fredholm operator, index, weighted Lebesgue space, piecewise almost periodic symbols