On integro-functional operators with a shift which is not one-to-one

Functional and singular integro-functional operators with nonunivalent shift are considered. The spectrum of a weighted shift operator in the space $L_p(\Gamma)$, $1\leqslant p\leqslant\infty$, is studied in the case where the shift is an expanding nonunivalent mapping of a smooth finite-dimensional mapping of a manifold $\Gamma$. Necessary and sufficient conditions for the Fredholm property are obtained, as well as a formula for computing the index of a singular integral operator with nonunivalent expanding shift of the unit circle.
Bibliography: 17 titles.