Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Feng, De-Jun, Yi, Tian-Han
Institution: Chinese University of Hong Kong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214024557