<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karlovich, Alexei Yu.</style></author><author><style face="normal" font="default" size="100%">Karlovich, Yuri I.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces</style></title><secondary-title><style face="normal" font="default" size="100%">Integral Equations and Operator Theory</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2002</style></year><pub-dates><date><style  face="normal" font="default" size="100%">{FEB}</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/article/10.1007/BF01275516</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">{2}</style></number><publisher><style face="normal" font="default" size="100%">{BIRKHAUSER VERLAG AG}</style></publisher><pub-location><style face="normal" font="default" size="100%">{VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND}</style></pub-location><volume><style face="normal" font="default" size="100%">42</style></volume><pages><style face="normal" font="default" size="100%">201-228</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'&gt;&lt;/script&gt;&lt;p&gt;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&lt;br /&gt;
\[&lt;br /&gt;
0&amp;lt;\alpha_X=p_X\le q_X=\beta_X&amp;lt;1.&lt;br /&gt;
\]&lt;/p&gt;
</style></abstract><work-type><style face="normal" font="default" size="100%">{Article}</style></work-type></record></records></xml>