On Convolution Squares of Singular Measures

Chan, Vincent
Subject Keywords: convolution square, singular measure, Lipschitz, Hausdorff dimension, Pure Mathematics
Date: 2010-08-25 (submitted on: 2010)

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 $\alpha-1/2$.
Program: Pure Mathematics
Department: Pure Mathematics
Degree: Master of Mathematics
URI: http://hdl.handle.net/10012/5369

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