On the Beurling dimension of exponential frames

TL;DR

This paper investigates the relationship between the Beurling dimension of Fourier exponential frames and the Hausdorff dimension of fractal measures generated by affine iterated function systems, establishing their equality under certain conditions.

Contribution

It proves that, under a mild condition, the Beurling dimension of Fourier frames on fractals equals the fractal's Hausdorff dimension, linking harmonic analysis and fractal geometry.

Findings

Beurling dimension of Fourier frames matches Hausdorff dimension of fractals

Established equality under mild technical conditions

Connects Fourier analysis with fractal measure geometry

Abstract

We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff dimension of the fractal.