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

2022/05/06 by M. Aloisio, Aloisio, M., Sérgio Luís de Carvalho +5 · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2205.03489

Abstract

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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• Hölder continuity and Fourier asymptotics of spectral measures for 1D Schrödinger operators under exponentially decaying perturbations

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