Symmetries in projective multiresolution analyses

TL;DR

This paper extends Packer and Rieffel's theorem to include symmetries, providing conditions for invariant wavelets in projective multiresolution analyses with finite group actions.

Contribution

It introduces an equivariant version of the theorem, establishing conditions for the existence of symmetric wavelets in projective multiresolution frameworks.

Findings

Provides sufficient conditions for symmetric wavelet existence

Extends previous theorems to include finite group invariance

Ensures invariance of wavelets under group actions

Abstract

We give an equivariant version of Packer and Rieffel's theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analyses. The scaling functions that generate a projective multiresolution analysis are supposed to be invariant with respect to some finite group action. We give sufficient conditions for the existence of wavelets with similar invariance.