标题： 自相似集上自相似测度的傅里叶变换衰减率的显式上界 显示英文标题

标题： Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets

摘要： 傅立叶变换在分形集上的概率测度的研究在最近的研究中起着重要作用。 更快的衰减率已知在度量数论等领域能产生更好的结果。 本文专注于定义在自相似集上的自相似概率测度。 为其衰减率推导出了显式的上界，改进了以前的研究。 这些成果通过一个应用来说明，即对Lüroth表示中的数字被限制在一个有限集合中的数集。 显示英文摘要

摘要： The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on self-similar probability measures defined on self-similar sets. Explicit upper bounds are derived for their decay rates, improving upon prior research. These findings are illustrated with an application to sets of numbers whose digits in their L\"uroth representations are restricted to a finite set.