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- W3206070744 abstract "We show that the Szegő matrices, associated with Verblunsky coefficients $${{alpha }_n}_{nin {{mathbb {Z}}}_+}$$ 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 $$1 - {gamma }$$ . In particular, the singular part of the associated probability measure on the unit circle is supported by a set of Hausdorff dimension no more than $$1-{gamma }$$ . This proves the OPUC Hausdorff dimension conjecture of Barry Simon from 2005." @default.
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- W3206070744 date "2021-10-18" @default.
- W3206070744 modified "2023-10-18" @default.
- W3206070744 title "Simon’s OPUC Hausdorff dimension conjecture" @default.
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- W3206070744 doi "https://doi.org/10.1007/s00208-021-02283-7" @default.
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