Citation
Hungerford, Gregory Jude (1988) Boundaries of Smooth Sets and Singular Sets of Blaschke Products in the Little Bloch Class. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ehgq-c421. https://resolver.caltech.edu/CaltechTHESIS:10232009-113530661
Abstract
A subset of R is called smooth if the integral of its characteristic function is smooth in the sense defined by Zygmund. It is shown that such a set is either trivial or its boundary has Hausdorff dimension 1. Sets are constructed here which are as close to smooth as one likes but whose boundaries do not have dimension 1.
It was conjectured by T. Wolff that if B is Blaschke product in the Little Bloch class, its zeroes accumulate to a set of dimension 1. This conjecture is proven here.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | Mathematics |
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Thesis Availability: | Public (worldwide access) |
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| Thesis Committee: |
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| Defense Date: | 16 May 1988 |
| Record Number: | CaltechTHESIS:10232009-113530661 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:10232009-113530661 |
| DOI: | 10.7907/ehgq-c421 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 5326 |
| Collection: | CaltechTHESIS |
| Deposited By: | Tony Diaz |
| Deposited On: | 26 Oct 2009 16:03 |
| Last Modified: | 16 Apr 2021 22:24 |
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