On Convolution Squares of Singular Measures

Thumbnail Image

Date

2010-08-25T15:09:12Z

Authors

Chan, Vincent

Advisor

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$.

Description

Keywords

convolution square, singular measure, Lipschitz, Hausdorff dimension

LC Subject Headings

Citation