Obtaining the Fourier spectrum via Fourier coefficients

Fuente: arXiv
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Main Authors: Carnovale, Marc, Fraser, Jonathan M., de Orellana, Ana E.
Format: Preprint
Published: 2024
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author Carnovale, Marc
Fraser, Jonathan M.
de Orellana, Ana E.
author_facet Carnovale, Marc
Fraser, Jonathan M.
de Orellana, Ana E.
contents 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
format Preprint
id arxiv_https___arxiv_org_abs_2403_12603
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Obtaining the Fourier spectrum via Fourier coefficients
Carnovale, Marc
Fraser, Jonathan M.
de Orellana, Ana E.
Classical Analysis and ODEs
Functional Analysis
primary: 28A75, 42B10, secondary: 42B05
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
title Obtaining the Fourier spectrum via Fourier coefficients
topic Classical Analysis and ODEs
Functional Analysis
primary: 28A75, 42B10, secondary: 42B05
url https://arxiv.org/abs/2403.12603