Projective multi-resolution analyses arising from direct limits of Hilbert modules - Larsen, Nadia S.; Raeburn, Iain (Mathematica Scandinavica, 2007)
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.