2019/04/09 by Quentin Menet, Menet, Quentin · 1 citation
Mathematics · #47A16 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1904.04818
openalex publication_date 2019/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given A the family of weights a=(an)n decreasing to 0 such that the series ∑n=0∞ an diverges, we show that the supremum on A of lower weighted densities coincides with the unweighted upper density and that the infimum on A of upper weighted densities coincides with the unweighted lower density. We then investigate the notions of U-frequent hypercyclicity and frequent hypercyclicity associated to these weighted densities. We show that there exists an operator which is U-frequently hypercyclic for each weight in A but not frequently hypercyclic, although the set of frequently hypercyclic vectors always coincides with the intersection of sets of U-frequently hypercyclic vectors for each weight in A.