发表机构
The Chinese University of Hong Kong（香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整刻画了傅里叶变换不趋于零的齐次自仿测度，证明整数自仿测度具有幂次傅里叶衰减等价于绝对连续，并给出判定绝对连续概率向量的算法。
AI 中文摘要
我们给出了傅里叶变换在无穷远处不趋于$0$的齐次自仿测度的完整代数刻画。此外，我们证明了一个整数自仿测度具有幂次傅里叶衰减当且仅当它是绝对连续的。对于给定的整数仿射迭代函数系，我们还提供了一种算法，用于确定那些使得相关自仿测度绝对连续的概率向量。
英文摘要
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.
