Simon's OPUC Hausdorff Dimension Conjecture

David Damanik, Shuzheng Guo, Darren C. Ong

We show that the Szegő 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 b…