2024/03/19 by Carnovale, Marc, Fraser, Jonathan M., de Orellana, Ana E.
#42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #primary: 28A75 #secondary: 42B05
paper · doi:10.48550/arxiv.2403.12603
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