A panoramic view of groupoids and MRAs
Marius Ionescu, Paul S. Muhly
TL;DR
This paper employs groupoid theory to offer new proofs of Mallat's theorems on multiresolution analyses, extending their applicability to broader mathematical contexts.
Contribution
It introduces novel groupoid-based proofs of key theorems in wavelet theory, expanding their scope beyond traditional frameworks.
Findings
New proofs of Mallat's theorems using groupoid technology
Extension of multiresolution analysis concepts to broader contexts
Connections to existing work by Raeburn and co-authors
Abstract
This sequel to \cite{im2008} uses groupoid technology to provide new proofs of the famous theorems of Mallat \cite[Theorem 1 and 2]{Mall_TAMS89} that extend to much broader contexts than those conceived by Mallat. This work was inspired in large part by \cite{Bagg_co_JFAA09,Bag_co_JFA10,LarRae_CM06,Larsen-Raeburn2007}, written by Iain Raeburn and co-authors.
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