Obtaining the Fourier spectrum via Fourier coefficients
Classical Analysis and ODEs
2024-03-20 v1 Functional Analysis
Abstract
The Fourier spectrum is a family of dimensions that interpolates between the Fourier and Hausdorff dimensions and are defined in terms of certain energies which capture Fourier decay. In this paper we obtain a convenient discrete representation of those energies using the 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
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Cite
@article{arxiv.2403.12603,
title = {Obtaining the Fourier spectrum via Fourier coefficients},
author = {Marc Carnovale and Jonathan M. Fraser and Ana E. de Orellana},
journal= {arXiv preprint arXiv:2403.12603},
year = {2024}
}
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13 pages