Are MSF wavelets minimally supported?

TL;DR

This paper proves that the Fourier transform of any wavelet must contain a wavelet set, addressing Larson's problem and expanding understanding of wavelet support properties.

Contribution

It provides an affirmative answer to a non-measurable variant of Larson's problem, showing wavelet Fourier transforms must contain wavelet sets.

Findings

Fourier transform of a wavelet must contain a wavelet set

Addresses a non-measurable variant of Larson's problem

Proposes two new related problems

Abstract

Larson's problem asks ``Must the support of the Fourier transform of a wavelet contain a wavelet set?". We give an affirmative answer to a non-measurable variant of this question by proving that the Fourier transform of a wavelet must contain a possibly non-measurable wavelet set. We also provide background results on Larson's problem and propose two new related problems.