One-Sided Invertibility Criteria for Binomial Functional Operators with Shift and Slowly Oscillating Data

Let α be an orientation-preserving homeomorphism of [ 0 , ∞] onto itself with only two fixed points at 0 and ∞, whose restriction to R₊= (0 , ∞) is a diffeomorphism, and let U_α be the corresponding isometric shift operator acting on the Lebesgue space L^p(R₊) by the rule Uαf=(α′)1/p(f∘α). We prove criteria for the one-sided invertibility of the binomial functional operator aI- bU_α on the spaces L^p(R₊) , p∈ (1 , ∞) , under the assumptions that a, b and α^′ are bounded and continuous on R₊ and may have slowly oscillating discontinuities at 0 and ∞.