Geodesic
Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle
Ars Inveniendi Analytica (2021)

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We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions of these sets. As a corollary of the higher-dimensional results we obtain some new cases of the fractal uncertainty principle in odd dimensions.
Publié le :
DOI : 10.15781/gw9q-k252 
@article{10_15781_gw9q_k252,
     author = {Laura Cladek and Terence Tao},
     title = {Additive energy of regular measures in one and higher dimensions, and
  the fractal uncertainty principle},
     journal = {Ars Inveniendi Analytica},
     publisher = {mathdoc},
     year = {2021},
     doi = {10.15781/gw9q-k252},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.15781/gw9q-k252/}
}
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  the fractal uncertainty principle
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Laura Cladek; Terence Tao. Additive energy of regular measures in one and higher dimensions, and
  the fractal uncertainty principle. Ars Inveniendi Analytica (2021). doi: 10.15781/gw9q-k252

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