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

Authors

  • Nadia S. Larsen
  • Iain Raeburn

DOI:

https://doi.org/10.7146/math.scand.a-15026

Abstract

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

Downloads

Published

2007-06-01

How to Cite

Larsen, N. S., & Raeburn, I. (2007). Projective multi-resolution analyses arising from direct limits of Hilbert modules. MATHEMATICA SCANDINAVICA, 100(2), 317–360. https://doi.org/10.7146/math.scand.a-15026

Issue

Section

Articles