Geodesic
On Convolutions of Convex Sets and Related Problems
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 877-883

Voir la notice de l'article provenant de la source Cambridge University Press

We prove some results concerning convolutions, additive energies, and sumsets of convex sets and their generalizations. In particular, we show that if a set $A\,=\,{{\{{{a}_{1}},\,.\,.\,.\,,\,{{a}_{n}}\}}_{<}}\,\subseteq \,\mathbb{R}$ has the property that for every fixed $1\,\le \,d\,<\,n$ , all differences ${{a}_{i}}\,-\,{{a}_{i-d}},\,d\,<\,i\, , are distinct, then $\left| A\,+\,A \right|\,\gg \,{{\left| A \right|}^{3/2+c}}$ for a constant $c\,>\,0$ .
DOI : 10.4153/CMB-2013-041-8
Mots-clés : 11B99, convex sets, additive energy, sumsets 
Schoen, Tomasz. On Convolutions of Convex Sets and Related Problems. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 877-883. doi: 10.4153/CMB-2013-041-8
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