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

Nadia S. Larsen·Iain Raeburn
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Abstract

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over $C^*$-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 $\R^n$. 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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BibTeXRIS

Nadia S. Larsen, Iain Raeburn. 2007-01-10. Projective multi-resolution analyses arising from direct limits of Hilbert modules. https://arxiv.org/abs/math/0701276

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