标题： 关于奇异测度谱中的有限配置 显示英文标题

标题： On finite configurations in the spectra of singular measures

摘要： 我们建立以下确定性原理的各种形式：如果$S$是$\mathbb{R}^{n}$上一个足够奇异的概率测度的傅里叶变换的支持，则集合$S \subset \mathbb{R}^{n}$包含一个给定的有限线性模式。 作为其主要推论，我们提供了PDE和傅里叶约束向量测度的新维数估计。 在由齐次算子给出的某些限制情况下，这些结果改进了与$k$-波锥概念相关的已知界限。 显示英文摘要

摘要： We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure on $\mathbb{R}^{n}$. As its main corollary, we provide new dimensional estimates for PDE- and Fourier-constrained vector measures. Those results, in certain cases of restrictions given by homogeneous operators, improve known bounds related to the notion of the $k$-wave cone.