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One-sided invertibility of binomial functional operators with a shift in rearrangement-invariant spaces

A. Karlovich·Yu. Karlovich
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Abstract

Let $Γ$ be an oriented Jordan smooth curve and $α$ be a diffeomorphism of $Γ$ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertiblity of the binomial functional operator \[ A=aI-bW \] where $a$ and $b$ are continuous functions, $I$ is the identity operator, $W$ is the shift operator $Wf=f\circα$, in a reflexive rearrangement-invariant space $X(Γ)$ with Boyd indices $α_X,β_X$ and Zippin indices $p_X,q_X$ satisfying inequalities \[ 0<α_X=p_X\le q_X=q_X<1. \]

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A. Karlovich, Yu. Karlovich. 2000-10-17. One-sided invertibility of binomial functional operators with a shift in rearrangement-invariant spaces. https://arxiv.org/abs/math/0010171

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