Reduction of singular integral operators with flip and their Fredholm property (Q2378861)

This paper studies singular integral operators with a reverting orientation Carleman shift. It proves that such an operator is equivalent to the sum of a matrix Toeplitz operator and a Hankel operator. Furthermore, it provides necessary and sufficient conditions for their Fredholm properties in two cases, the case of continuous and piecewise continuous coefficients and the case of semi-almost-periodic coefficients.