Abstract
Let Γ be an oriented Jordan smooth curve and α a diffeomorphism of Γ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator
wherea andb are continuous functions,I is the identity operator,W is the shift operator,Wf=foα, on a reflexive rearrangement-invariant spaceX(Γ) with Boyd indices α X , β X and Zippin indicesp x,q x satisfying inequalities
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Partially supported by F.C.T. (Portugal) grant PRAXIS XXI/BPD/22006/99.
Partially supported by CONCACYT (México) grant, Cátedra Patrimonial, No. 990017-EX., nivel II.
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Karlovich, A.Y., Karlovich, Y.I. One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces. Integr equ oper theory 42, 201–228 (2002). https://doi.org/10.1007/BF01275516
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DOI: https://doi.org/10.1007/BF01275516