标题： 关于西蒙的豪斯多夫维数猜想 显示英文标题

标题： On Simon's Hausdorff Dimension Conjecture

摘要： 巴里·西蒙在2005年提出猜想，与维布伦斯基系数$\{\alpha_n\}_{n\in\mathbb{Z}_+}$相关的塞戈矩阵，在满足$\sum_{n = 0}^\infty n^\gamma |\alpha_n|^2 < \infty$的某些$\gamma \in (0,1)$值时，对于超出一个豪斯多夫维数不超过$1 - \gamma$的集合之外的$z \in \partial \mathbb{D}$值是有界的。三位作者最近通过采用类似于克里斯蒂安·雷姆林对薛定谔算子所做的工作的普吕弗变量方法，证明了这个猜想。本文是一篇配套文章，提出了西蒙猜想的一个较弱版本的简单证明，该证明遵循西蒙另一个猜想的证明精神。 显示英文摘要

摘要： Barry Simon conjectured in 2005 that the Szeg\H{o} matrices, associated with Verblunsky coefficients $\{\alpha_n\}_{n\in\mathbb{Z}_+}$ obeying $\sum_{n = 0}^\infty n^\gamma |\alpha_n|^2 < \infty$ for some $\gamma \in (0,1)$, are bounded for values $z \in \partial \mathbb{D}$ outside a set of Hausdorff dimension no more than $1 - \gamma$. Three of the authors recently proved this conjecture by employing a Pr\"ufer variable approach that is analogous to work Christian Remling did on Schr\"odinger operators. This paper is a companion piece that presents a simple proof of a weak version of Simon's conjecture that is in the spirit of a proof of a different conjecture of Simon.