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

2007/01/10 by Nadia S. Larsen, Larsen, Nadia S., Iain Raeburn +1 · 1 citation
Mathematics · #42C15 #46L99 #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:42C15 #msc:46L99

paper · pdf · doi:10.48550/arxiv.math/0701276

arxiv created 2007/01/10 · openalex publication_date 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Crossed products by abelian semigroups via transfer operators

Cited by

• A panoramic view of groupoids and MRAs

Related

• Projective multiresolution analyses for L²(R²)
• Direct limits, multiresolution analyses, and wavelets
• Wavelet filter functions, the matrix completion problem, and projective modules over C(\mathbb Tⁿ)
• Wavelets and Hilbert modules
• Projective multiresolution analyses for dilations in higher dimensions