Square summability of variations and convergence of the transfer operator

Abstract

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 [13], 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 [7]. We also prove uniqueness of so-called G-measures, introduced by Brown and Dooley [2], under square summability of variations.

8 pages

Cited by in corpus (2)

• Unique Bernoulli g-measures
• Phase Transitions in One-dimensional Translation Invariant Systems: a Ruelle Operator Approach