论文标题
使用四位数元素的光谱自相似度量分类
Classification of spectral self-similar measures with four-digit elements
论文作者
论文摘要
令$μ$为迭代功能系统产生的一个自相似度量，该功能系统的四个地图相等收缩比$ 0 <ρ<1 $。我们研究$μ$是一种光谱度量，这意味着它在$ l^2（μ）$中接受指数正顺式基础$ \ {e^{2πiλx} \} _ {λ\inλ} $。通过将许多作者的先前结果结合在一起，并仔细研究了一些新案例，我们将所有光谱自相似的度量与四个地图完全分类。此外，该案件使我们能够提出一个经过改进的奥巴瓦猜想，即在一般情况下，自相似措施何时是光谱。
Let $μ$ be a self-similar measure generated by iterated function system of four maps of equal contraction ratio $0<ρ<1$. We study when $μ$ is a spectral measure which means that it admits an exponential orthonormal basis $\{e^{2πi λx}\}_{λ\inΛ}$ in $L^2(μ)$. By combining previous results of many authors and a careful study of some new cases, we completely classify all spectral self-similar measures with four maps. Moreover, the case allows us to propose a modified Łaba-Wang conjecture concerning when the self-similar measures are spectral in general cases.
