On Convolutions of Convex Sets and Related Problems

Canadian mathematical bulletin

Tomasz Schoen¹ 

[1] Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

关键词: convex sets;    additive energy;    sumsets;   

DOI  :  10.4153/CMB-2013-041-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove some results concerning covolutions, theadditive energy and sumsets of convex sets and its generalizations. Inparticular, we show that if a set $A={a_1,dots,a_n}_lt subseteq mathbb R$ hasthe property that for every fixed $1leqslant dlt n,$ all differences $a_i-a_{i-d}$, $dlt ilt n,$ are distinct, then$|A+A|gg |A|^{3/2+c}$ for a constant $cgt 0.$

【 授权许可】

Unknown