Square Summability of Variations and Convergence of the Transfer Operator
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
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.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-23779DOI: 10.1017/S0143385707000788ISI: 000258204900006OAI: oai:DiVA.org:uu-23779DiVA: diva2:51553