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 L2(R). Here they investigate similar constructions in the context of Hilbert modules over C-algebras. For modules over C(Tn), the results shed light on work of Packer and Rieffel on projective multi-resolution analyses for specific Hilbert C(Tn)-modules of functions on Rn. There are also new applications to modules over C(C) when C is the infinite path space of a directed graph.

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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

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Section

Articles