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A natural space of functions for the Ruelle operator theorem
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Walters, Peter, 1943. (2007) A natural space of functions for the Ruelle operator theorem. Ergodic Theory and Dynamical Systems, Vol.27 (No.4). pp. 13231348. ISSN 01433857

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Official URL: http://dx.doi.org/10.1017/S0143385707000028
Abstract
We study a new space, $R(X)$, of realvalued 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 bisequences of zeros and ones.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Ruelle operators, Transfer operators, Operator theory 
Journal or Publication Title:  Ergodic Theory and Dynamical Systems 
Publisher:  Cambridge University Press 
ISSN:  01433857 
Official Date:  22 June 2007 
Volume:  Vol.27 
Number:  No.4 
Page Range:  pp. 13231348 
Identification Number:  10.1017/S0143385707000028 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  T. Bousch. La condition de Walters. Ann. Sci. ´Ecole Norm. Sup. (4) 34 (2001), 287–311. 
URI:  http://wrap.warwick.ac.uk/id/eprint/658 
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