Diffraction theory and almost periodic distributions
Author
Faculty Advisor
Date
2016
Keywords
tempered distributions, autocorrelation, almost periodicity
Abstract (summary)
We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distrubution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones. We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lesbegue decomposition, with the Fourier-Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.
Publication Information
Strungaru, N., & Terauds, V. (2016). Diffraction theory and almost periodic distributions. arXiv:1603.04796v1. https://arxiv.org/abs/1603.04796
DOI
Notes
Item Type
Report
Language
English
Rights
All Rights Reserved