关键词: Topologically multiple recurrence, recurrence, hypercyclicity, locally compact group, L^p-space

Abstract:

Let G be a locally compact group, and let 1≤p<∞. We characterize topologically multiply recurrent weighted translation operators on L^p(G) in terms of the Haar measure and the weight function. We also show that there do not exist any recurrent weighted translation operators on L^∞(G).

Key words: Topologically multiple recurrence, recurrence, hypercyclicity, locally compact group, L^p-space