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(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.