2022/05/21 by Noureddine Karim, Karim, Noureddine, Otmane Benchiheb +3
Mathematics · #46A99 #47A16 #Advanced Topology and Set Theory #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2205.10638
openalex publication_date 2022/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Furstenberg family F is a collection of infinite subsets of the set of positive integers such that if A⊂ B and A∈ F, then B∈ F. For a Furstenberg family F, finitely many operators T1,...,TN acting on a common topological vector space X are said to be disjoint F-transitive if for every non-empty open subsets U0,...,UN of X the set \n∈ ℕ: U0 ∩ T1-n(U1)∩...∩ TN-n(UN)≠∅\ belongs to F. In this paper, depending on the topological properties of Ω, we characterize the disjoint F-transitivity of N≥2 composition operators Cϕ1,…,CϕN acting on the space H(Ω) of holomorphic maps on a domain Ω⊂ ℂ by establishing a necessary and sufficient condition in terms of their symbols ϕ1,...,ϕN.