Criteria for one-sided invertibility of a functional operator in rearrangement-invariant spaces of fundamental type

Citation:
Karlovich, Alexei Yu. "Criteria for one-sided invertibility of a functional operator in rearrangement-invariant spaces of fundamental type." Mathematische Nachrichten. 229 (2001): 91-118.

Abstract:

Let \(\gamma\) be a simple open smooth curve and \(\alpha\) be an orientation-preserving diffeomorphism of \(\gamma\) onto itself which has only two fixed points. Criteria for one-sided invertibility of the functional operator
\[
A=aI-bW,
\]
where \(a\) and \(b\) are continuous functions, \(I\) is the identity operator, \(W\) is the shift operator: \((Wf)(t)=f[\alpha(t)]\), in a reflexive rearrangement-invariant space of fundamental type \(X(\gamma)\) with nontrivial Boyd indices, are obtained.

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