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Square summability of variations and convergence of the transfer operator
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik. (Matematik)
Department of Mathematics, Uppsala University, Uppsala, Sweden.
2008 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 28, no 4, p. 1145-1151Article 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(1) (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. Öberg. 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, p. 1145-1151
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-2222DOI: 10.1017/S0143385707000788ISI: 000258204900006Scopus ID: 2-s2.0-47249141936OAI: oai:DiVA.org:hig-2222DiVA, id: diva2:118884
Available from: 2008-09-18 Created: 2008-09-18 Last updated: 2018-03-13Bibliographically approved

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