The local trace function for super-wavelets

Details The local trace function for super-wavelets The local trace function for super-wavelets

2005-11-05

arxiv.org/abs/math/0511143v1

Wavelets, frames and operator theory}, 115--136, eds: C.Heil, P.Jorgensen, D.Larson, Proceedings of the 2003 annual AMS meetin

Mathematics

Functional Analysis

Scientific paper

We define an affine structure on $\ltwor\oplus...\oplus\ltwor$ and, following some ideas developed in \cite{Dut1}, we construct a local trace function for this situation. This trace function is a complete invariant for a shift invariant subspace and it has a variety of properties which make it easily computable. The local trace is then used to give a characterization of super-wavelets and to analyze their multiplicity function, dimension function and spectral function. The "$n\times$" oversampling result of Chui and Shi \cite{CS} is refined to produce super-wavelets.

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