PreprintarXiv licencearXiv
On the Rajchman property of homogeneous self-affine measures
Abstract
We provide a complete algebraic characterization of homogeneous self-affine measures whose Fourier transform does not tend to $0$ at infinity. Moreover, we prove that an integral self-affine measure has power Fourier decay if and only if it is absolutely continuous. For a given integral affine IFS, we also provide an algorithm for determining those probability vectors for which the associated self-affine measure is absolutely continuous.
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BibTeX
@misc{feng2026rajchman,
title = {{On the Rajchman property of homogeneous self-affine measures}},
author = {De-Jun Feng and Tian-Han Yi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23474},
eprint = {2609.23474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23474},
}
RIS
TY - UNPB
TI - On the Rajchman property of homogeneous self-affine measures
AU - De-Jun Feng
AU - Tian-Han Yi
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23474
UR - https://arxiv.org/abs/2609.23474
AB - We provide a complete algebraic characterization of homogeneous self-affine measures whose Fourier transform does not tend to $0$ at infinity. Moreover, we prove that an integral self-affine measure has power Fourier decay if and only if it is absolutely continuous. For a given integral affine IFS, we also provide an algorithm for determining those probability vectors for which the associated self-affine measure is absolutely continuous.
ER -