2024/12/23 by Hu, Zongrui, Ma, Xiao, Xu, Leiye +1
#37A15 #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2412.17409
In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As applications: 1) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it has bounded mean-complexity along Følner sequences; 2) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it is mean equicontinuous along a tempered Følner sequence, or equicontinuous in the mean along a tempered Følner sequence.