We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
AUTOMATIC SEQUENCES AS GOOD WEIGHTS FOR ERGODIC THEOREMS.
- Authors
Eisner, Tanja; Konieczny, Jakub
- Abstract
We study correlation estimates of automatic sequences (that is, sequences computable by finite automata) with polynomial phases. As a consequence, we provide a new class of good weights for classical and polynomial ergodic theorems. We show that automatic sequences are good weights in L2 for polynomial averages and totally ergodic systems. For totally balanced automatic sequences (i.e., sequences converging to zero in mean along arithmetic progressions) the pointwise weighted ergodic theorem in L1 holds. Moreover, invertible automatic sequences are good weights for the pointwise polynomial ergodic theorem in Lr, r > 1.
- Subjects
MATHEMATICAL sequences; ERGODIC theory; MARK I (Calculator); ARITHMETIC series; POLYNOMIALS
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2018, Vol 38, Issue 8, p4087
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2018178