Obtaining the Fourier spectrum via Fourier coefficients
Abstract
The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and is defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete representation of those energies using Fourier coefficients. As an example application, we use this representation to establish sharp bounds for the Fourier spectrum of a general measure with bounded support, improving previous estimates of the second-named author.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 2005–2017
- Publication date
- 14 January 2026
- Language
- EN