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 Uα be the corresponding isometric shift operator acting on the Lebesgue space Lp(R+) by the rule Uαf=(α′)1/p(f∘α). We prove criteria for the one-sided invertibility of the binomial functional operator aI- bUα on the spaces Lp(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 ∞.
- limit operator
- one-sided invertibility
- Orientation-preserving non-Carleman shift
- slowly oscillating function