Projective multiresolution analyses over irrational rotation algebras

摘要

This paper takes the idea of projective multiresolution analyses and extends it to modules over noncommutative C*-algebras, particularly irrational rotation algebras, by constructing a concrete example. We discuss previous definitons due to J. Packer and M. Rieffel, and modify these definitions to account for our specific situation. Then the projective multiresolution analysis is built, using the framework of a Morita equivalence due to M. Rieffel and employing a scaling function due to I. Daubechies. Finally, the paper ends by using the projective multiresolution analysis to construct a module frame for a Hilbert module over an irrational rotation algebra, and using the module frame to create an explicit isomorphism to a well-known Hilbert module.