Simple wavelet sets in R^n

Abstract

Wavelet sets that are finite unions of convex sets are constructed in ${\mathbb{R}}^n$, $n\ge 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt{n}$. In particular, we produce simple wavelet sets in any dimension for dilation by any real scalar greater than 1.

To appear in Journal of Geometric Analysis; 13 pages, 10 figures