English

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: ax1+bx2=cy1+dy2ax_1 +bx_2= cy_1+dy_2. 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.

Keywords

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}
}
R2 v1 2026-06-28T19:54:30.007Z