@article { ISI:000173515700006, title = {One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces}, journal = {Integral Equations and Operator Theory}, volume = {42}, number = {{2}}, year = {2002}, month = {{FEB}}, pages = {201-228}, publisher = {{BIRKHAUSER VERLAG AG}}, type = {{Article}}, address = {{VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND}}, abstract = {

Let \(\Gamma\) be an oriented Jordan smooth curve and \(\alpha\) a diffeomorphism of $\Gamma$ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility 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, \(Wf=f\circ\alpha\), on a reflexive rearrangement-invariant space \(X(\Gamma)\) with Boyd indices \(\alpha_X,\beta_X\) and Zippin indices \(p_X,q_X\) satisfying inequalities
\[
0\<\alpha_X=p_X\le q_X=\beta_X\<1.
\]

}, issn = {{0378-620X}}, doi = {{10.1007/BF01275516}}, url = {http://link.springer.com/article/10.1007/BF01275516}, author = {Karlovich, Alexei Yu. and Karlovich, Yuri I.} }