Projective multi-resolution analyses arising from direct limits of Hilbert modules

Abstract

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\mathbb{R})$. Here they investigate similar constructions in the context of Hilbert modules over $C^{\ast }$-algebras. For modules over $C(\T^n)$, the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert $C(\T^n)$-modules of functions on ${\mathbb{R}}^n$. There are also new applications to modules over $C(C)$ when $C$ is the infinite path space of a directed graph.

References in corpus (2)

• Crossed products by abelian semigroups via transfer operators
• The algebra of harmonic functions for a matrix-valued transfer operator