Notes on a theorem of Katznelson and Ornstein

• Main Authors: Akhadkulov, Habibulla, Dzhalilov, Akhtam, Khanin, Konstantin
• Format: Article
• Published: American Institute of Mathematical Sciences 2017
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://repo.uum.edu.my/23043/; http://doi.org/10.3934/dcds.2017197
• Institution: Universiti Utara Malaysia

Let logf′ be an absolutely continuous and f′′/f′∈Lp(S1,dℓ) for some p>1, where ℓ is Lebesgue measure. We show that there exists a subset of irrational numbers of unbounded type, such that for any element ρˆ of this subset, the linear rotation Rρˆ and the shift ft=f+tmod1, t∈[0,1) with rotation nu...