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

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DOI

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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     author = {Schoen, Tomasz},
     title = {On {Convolutions} of {Convex} {Sets} and {Related} {Problems}},
     journal = {Canadian mathematical bulletin},
     pages = {877--883},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2013-041-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-041-8/}
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