We use the Freiman theorem in arithmetic combinatorics to show that if the Fourier transform of certain measures satisfies sufficiently bad estimates, then the support of the measure possesses an additive structure. The result is then discussed in light of the Falconer distance problem.
|Translated title of the contribution||Frieman Theorem, Fourier transform, and additive structure of measures|
|Pages (from-to)||97 - 109|
|Number of pages||13|
|Journal||Journal of the Australian Mathematical Society|
|Volume||86, issue 1|
|Publication status||Published - Feb 2009|