Work

Obtaining the Fourier spectrum via Fourier coefficients

Year: 2026

Type: article

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.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17610

Authors: Marc Carnovale, Jonathan Fraser, Ana de Orellana

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, University of St Andrews

Awards: G7269511974, G8696683499

OpenAlex ID: W7124152879

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Cites: 10

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