Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition
Faculty Advisor
Date
2023
Keywords
almost periodic measures, Fourier transform of measures, Lebesgue decomposition
Abstract (summary)
In this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in has order at most 2d. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets.
Publication Information
Spindeler, T., & Strungaru, N. (2023). Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition. Mathematische Nachrichten 297(2), 716-740. https://doi.org/10.1002/mana.202100658
Notes
Item Type
Article
Language
Rights
Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)
