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Boundaries of smooth sets and singular sets of Blaschke products in the little Bloch class

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. http://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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Wolff, Thomas H.
Thesis Committee:
  • Wolff, Thomas H. (chair)
Defense Date:16 May 1988
Record Number:CaltechTHESIS:10232009-113530661
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:10232009-113530661
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:26 Dec 2012 03:18

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