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Distributional chaos for weighted translation operators on groups. (arXiv:1807.05191v1 [math.FA])

来源于:arXiv
In this paper, we initiate the study of distributional chaos for weighted translations on locally compact groups, and give a sufficient condition for such operators to be distributionally chaotic. We also investigate the set of distributionally irregular vectors of weighted translations from the views of modulus, cone, equivalent class and atom. In particular, we show that the set of distributionally irregular vectors is residual if the group is the integer. Besides, the equivalent class of distributionally irregular vectors is path connected if the field is complex. 查看全文>>