Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (2): 443-452.doi: 10.1016/S0252-9602(16)30011-X

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RECURRENCE FOR WEIGHTED TRANSLATIONS ON GROUPS

Chung-Chuan CHEN   

  1. Department of Mathematics Education, National Taichung University of Education, Taiwan
  • Received:2014-05-09 Revised:2015-06-17 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    The author is supported by MOST of Taiwan (MOST 104-2115-M-142-002-).

Abstract:

Let G be a locally compact group, and let 1≤p<∞. We characterize topologically multiply recurrent weighted translation operators on Lp(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, Lp-space

CLC Number: 

  • 37B20
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