Year: 2014
Type: preprint
Abstract: We investigate the interplay between the discrete restriction phenomenon and incidence theory. Two angles are explored. One is a refinement of the machinery developed by Thomas Wolff, which when combined with a recent subcritical estimate of Bourgain leads to new Strichartz estimates for irrational tori. The other one connects various additive energies with the Szemerédi-Trotter Theorem. The combination of the two approaches recovers the best known Strichartz estimates for the classical torus in dimensions $n\ge 3$, without any appeal to number theory.
Source: arXiv (Cornell University)
Author: Demeter, Ciprian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2130163530