论文标题
在西蒙的豪斯多夫维度上的猜想
On Simon's Hausdorff Dimension Conjecture
论文作者
论文摘要
巴里·西蒙（Barry Simon）于2005年推测，szegő矩阵与verblunsky系数$ \ {α_n\} _ {n \ in \ Mathbb {z} _+} （0,1）$，以$ z \ in \ partial \ mathbb {d} $外部的值$ z \的限制，一组Hausdorff尺寸不超过$1-γ$。最近，三位作者通过采用类似于Christian Remling对Schrödinger运营商所做的工作的Prüfer变量方法来证明了这一猜想。本文是一件伴侣作品，它呈现了西蒙（Simon）猜想的弱版本的简单证明，该证明本着证明西蒙（Simon）的不同猜想的精神。
Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients $\{α_n\}_{n\in\mathbb{Z}_+}$ obeying $\sum_{n = 0}^\infty n^γ|α_n|^2 < \infty$ for some $γ\in (0,1)$, are bounded for values $z \in \partial \mathbb{D}$ outside a set of Hausdorff dimension no more than $1 - γ$. Three of the authors recently proved this conjecture by employing a Prüfer variable approach that is analogous to work Christian Remling did on Schrödinger 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.
