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## A natural space of functions for the Ruelle operator theorem

### Abstract

We study a new space, \$R(X)\$, of real-valued continuous functions on the space \$X\$ of sequences of zeros and ones. We show exactly when the Ruelle operator theorem holds for such functions. Any \$g\$-function in \$R(X)\$ has a unique \$g\$-measure and powers of the corresponding transfer operator converge. We also show Bow\$(X,T)\neq W(X,T)\$ and relate this to the existence of bounded measurable coboundaries, which are not continuous coboundaries, for the shift on the space of bi-sequences of zeros and ones

Topics: QA
Publisher: Cambridge University Press
Year: 2007
OAI identifier: oai:wrap.warwick.ac.uk:658

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