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Diffraction of rotated measures
Abstract
Consider a translation-bounded measure on the line. We can rotate the measure, distributing the mass proportionally to the area, to create a two-dimensional rotationally invariant translation-bounded measure. We show that the diffraction of the two-dimensional object is the normalised rotation of the diffraction of the original measure. We discuss some examples and generalisation beyond d=2.
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BibTeX
@misc{mazac2026diffraction,
title = {{Diffraction of rotated measures}},
author = {Jan Mazáč and Nicolae Strungaru},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37992},
eprint = {2610.37992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37992},
}
RIS
TY - UNPB
TI - Diffraction of rotated measures
AU - Jan Mazáč
AU - Nicolae Strungaru
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37992
UR - https://arxiv.org/abs/2610.37992
AB - Consider a translation-bounded measure on the line. We can rotate the measure, distributing the mass proportionally to the area, to create a two-dimensional rotationally invariant translation-bounded measure. We show that the diffraction of the two-dimensional object is the normalised rotation of the diffraction of the original measure. We discuss some examples and generalisation beyond d=2.
ER -