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Square Summability of Variations and Convergence of the Transfer Operator
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2008 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 28, no 4, 1145-1151 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [P. Walters. Trans. Amer Math. Soc. 353(l) (2001), 327-347], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in our earlier work [A. Johansson and A. Oberg. Math. Res. Lett. 10(5-6) (2003), 587-601]. We also prove uniqueness of the so-called G-measures, introduced by Brown and Dooley [G. Brown and A. H. Dooley. Ergod. Th. & Dynam. Sys. 11 (1991), 279-307], under square summability of variations.

Place, publisher, year, edition, pages
2008. Vol. 28, no 4, 1145-1151 p.
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:uu:diva-23779DOI: 10.1017/S0143385707000788ISI: 000258204900006OAI: oai:DiVA.org:uu-23779DiVA: diva2:51553
Available from: 2008-08-16 Created: 2008-08-16 Last updated: 2010-07-02Bibliographically approved

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