Kathryn Hare,Pure Math Department, University of Waterloo
“Local dimensions of convolutions of measures”
It is well known that the set of attainable values for the local dimensions of self-similar measures satisfying the open set condition is a closed interval. In contrast, Hu and Lau discovered the surprising fact that the 3-fold convolution of the classical Cantor measure has an isolated point in its set of attainable local dimensions. We will see that this property holds, more generally, for convolution powers of continuous, probability measures that satisfy modest assumptions.
MC 5403