Fourier Dimension and Translation Invariant Linear Equations
Classical Analysis and ODEs
2024-11-12 v1
Abstract
We consider a translation invariant linear equation in four variables with integer coefficients of the form: . The main result of the paper states that any set on the real line with Fourier dimension greater than 1/2 must contain a nontrivial solution of such an equation.
Cite
@article{arxiv.2411.06302,
title = {Fourier Dimension and Translation Invariant Linear Equations},
author = {Angel D. Cruz},
journal= {arXiv preprint arXiv:2411.06302},
year = {2024}
}