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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (2): 39-43.doi: 10.6040/j.issn.1671-9352.0.2016.125

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有限Abel群中的和集与Bohr集的子集

李芳,关爱霞,李国全*   

  1. 天津师范大学数学科学学院, 天津 300387
  • 收稿日期:2016-03-25 出版日期:2017-02-20 发布日期:2017-01-18
  • 通讯作者: 李国全(1969— ),男,教授,研究方向为调和分析与极值集合论. E-mail: lgq6964@263.net E-mail:18234105851@163.com
  • 作者简介:李芳(1990— ),女,硕士研究生,研究方向为极值集合论. E-mail: 18234105851@163.com

Sumsets and subsets of Bohr sets in finite abelian groups

LI Fang, GUANG Ai-xia, LI Guo-quan*   

  1. College of Mathematics Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2016-03-25 Online:2017-02-20 Published:2017-01-18

摘要: 对于有限Abel群GA,B⊂G,证明了存在Bohr集B(Γ,δ)与常数D>0满足: ∠T⊂B(Γ,δ),|T|≤D,A+B中含有T的平移

关键词: 对偶群, Bohr集, 和集

Abstract: Let G be a finite abelian group and A,B⊂G. It is proved that there exist a Bohr set B(Γ,δ)and a constant D>0 such that A+B contains a translate of any set T⊂B(Γ,δ)of size at most D.

Key words: sumset, dual group, Bohr set

中图分类号: 

  • O157.1
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[1] 曹亚萌,黎娇,李国全. 有限域上的和集与子空间的平移[J]. 山东大学学报(理学版), 2018, 53(4): 7-10.
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