A natural space of functions for the Ruelle operator theorem
Walters, Peter, 1943-. (2007) A natural space of functions for the Ruelle operator theorem. Ergodic Theory and Dynamical Systems, Vol.27 (No.4). pp. 1323-1348. ISSN 0143-3857
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Official URL: http://dx.doi.org/10.1017/S0143385707000028
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.
|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|
|Official Date:||22 June 2007|
|Page Range:||pp. 1323-1348|
|Access rights to Published version:||Open Access|
T. Bousch. La condition de Walters. Ann. Sci. ´Ecole Norm. Sup. (4) 34 (2001), 287–311.
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