We introduce a natural class of self-similar probability measures $\mu^{(r)} \ (0<r<1)$ on the real line $\mathbb{R}$, which we call the \emph{ Cantor convolutions}. They may be viewed as a triadic analogue of Bernoulli convolutions. Our main result proves that for parameters of the form $r=3^{-\beta}$ with $\beta>0$ badly approximable, the Cantor convolution $\mu^{(r)}$ has full Fourier dimension, $\dim_F(\mu^{(r)})=1.$ This is a joint work with Xiang Fang, Xueqing Ma and Hongli Zhang.
