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arXiv · 2403.12603

Obtaining the Fourier spectrum via Fourier coefficients

Marc Carnovale·Jonathan M. Fraser·Ana E. de Orellana
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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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Marc Carnovale, Jonathan M. Fraser, Ana E. de Orellana. 2024-03-19. Obtaining the Fourier spectrum via Fourier coefficients. https://arxiv.org/abs/2403.12603

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