Simple wavelet sets in R^n

TL;DR

This paper constructs simple wavelet sets in higher dimensions for specific expansive matrices, broadening the understanding of wavelet set structures in multivariate analysis.

Contribution

It introduces a method to construct finite unions of convex sets as wavelet sets in any dimension for certain expansive matrices.

Findings

Wavelet sets are constructed as finite unions of convex sets in R^n.

Applicable for dilation matrices with specific spectral properties.

Results hold for any real scalar greater than 1 in any dimension.

Abstract

Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, 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.