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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| container_title | Journal of mathematical physics |
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| creator | Aloisio, M. de Carvalho, S. L. de Oliveira, C. R. Souza, E. |
| description | 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. |
| doi_str_mv | 10.1063/5.0149320 |
| format | Article |
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| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2024-01, Vol.65 (1) |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_crossref_primary_10_1063_5_0149320 |
| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Fourier transforms Power law Singularities |
| title | On the Fourier asymptotics of absolutely continuous measures with power-law singularities |
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