Geodesic
An optimal $L^2$ autoconvolution inequality
Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 108-121

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

DOI

Let $\mathcal {F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb {R}_{\geq 0}$ such that $\int f = 1$. We determine the value of $\inf _{f \in \mathcal {F}} \| f \ast f \|_2^2$ up to a $4 \cdot 10^{-6}$ error, thereby making progress on a problem asked by Ben Green. Furthermore, we prove that a unique minimizer exists. As a corollary, we obtain improvements on the maximum size of $B_h[g]$ sets for $(g,h) \in \{ (2,2),(3,2),(4,2),(1,3),(1,4)\}$.
DOI : 10.4153/S0008439523000565
Mots-clés : Autoconvolution, Sidon set, additive energy 
White, Ethan Patrick. An optimal $L^2$ autoconvolution inequality. Canadian mathematical bulletin, Tome 67 (2024) no. 1, pp. 108-121. doi: 10.4153/S0008439523000565
@article{10_4153_S0008439523000565,
     author = {White, Ethan Patrick},
     title = {An optimal $L^2$ autoconvolution inequality},
     journal = {Canadian mathematical bulletin},
     pages = {108--121},
     year = {2024},
     volume = {67},
     number = {1},
     doi = {10.4153/S0008439523000565},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000565/}
}
TY  - JOUR
AU  - White, Ethan Patrick
TI  - An optimal $L^2$ autoconvolution inequality
JO  - Canadian mathematical bulletin
PY  - 2024
SP  - 108
EP  - 121
VL  - 67
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000565/
DO  - 10.4153/S0008439523000565
ID  - 10_4153_S0008439523000565
ER  - 
%0 Journal Article
%A White, Ethan Patrick
%T An optimal $L^2$ autoconvolution inequality
%J Canadian mathematical bulletin
%D 2024
%P 108-121
%V 67
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000565/
%R 10.4153/S0008439523000565
%F 10_4153_S0008439523000565

Cité par Sources :