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) |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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. |
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ISSN: | 0022-2488 1089-7658 |
DOI: | 10.1063/5.0149320 |