On the Fourier asymptotics of absolutely continuous measures with power-law singularities

We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon–Nikodym derivatives diverge with a power-law order. We also discuss an application...

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Veröffentlicht in:Journal of mathematical physics 2024-01, Vol.65 (1)
Hauptverfasser: Aloisio, M., de Carvalho, S. L., de Oliveira, C. R., Souza, E.
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon–Nikodym derivatives diverge with a power-law order. We also discuss an application to spectral measures of finite-rank perturbations of the discrete Laplacian.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0149320