Fourier decay and absolute continuity for typical homogeneous self-similar measures in ${\mathbb{R}}^d$ for $d\ge 3$

Boris Solomyak

We consider iterated function systems (IFS) in ${\mathbb{R}}^d$ for $d\ge 3$ of the form $\{f_j(x)=\lambda \mathcal{O}x+a_j{\}}_{j=0}^m$, with $a_0=0$ and $m\ge 1$. Here $\lambda \in (0,1)$ i…