@article { ISI:000171438800005, title = {Criteria for one-sided invertibility of a functional operator in rearrangement-invariant spaces of fundamental type}, journal = {Mathematische Nachrichten}, volume = {229}, year = {2001}, pages = {91-118}, publisher = {{WILEY-V C H VERLAG GMBH}}, type = {{Article}}, address = {{PO BOX 10 11 61, D-69451 WEINHEIM, GERMANY}}, 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.

}, keywords = {Boyd indices, one-sided invertibility, rearrangement-invariant space of fundamental type, Zippin indices}, {functional operator with shift}, issn = {{0025-584X}}, doi = {{10.1002/1522-2616(200109)229:1<91::AID-MANA91>3.3.CO;2-O}}, url = {http://onlinelibrary.wiley.com/doi/10.1002/1522-2616(200109)229:1\%3C91::AID-MANA91\%3E3.0.CO;2-X/abstract}, author = {Karlovich, Alexei Yu.} }