Γ-supercyclicity of families of translates in weighted Lp-spaces on locally compact groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:495

Article

Abbar, Arafat¹  Kuznetsova, Yulia² 

[1] Univ Paris Est Creteil, Univ Gustave Eiffel, LAMA, CNRS, F-77447 Marne La Vallee, France

[2] Univ Bourgogne Franche Comte, 16 Route Gray, F-25030 Besancon, France

关键词: Hypercyclicity;    Locally compact groups;    Supercyclicity;    Gamma-supercyclicity;    Translation semigroup;    Weighted spaces;   

DOI  :  10.1016/j.jmaa.2020.124709

来源: Elsevier

【 摘 要 】

Let omega be a weight function defined on a locally compact group G, 1 <= p < +infinity, S subset of G and let us assume that for any s is an element of S, the left translation operator T-s is continuous from the weighted L-p-space L-p(G, omega) into itself. For a given set Gamma subset of C, a vector f is an element of L-p(G, omega) is said to be (Gamma, S)-dense if the set {lambda T(s)f : lambda is an element of Gamma, s is an element of S} is dense in L-p(G, omega). In this paper, we characterize the existence of (Gamma, S)-dense vectors in L-p(G, omega) in terms of the weight and the set Gamma. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free