Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L 2 ( R d ) which have generalized multiresolutions. This means that the initial resolution subspace V 0 in L 2 ( R d ) is not singly generated. As a result, the representation of the integer lattice Z d restricted to V 0 has a nontrivial multiplicity function. We show how th...

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Bibliographic Details
Published in:Journal of mathematical physics 2005-08, Vol.46 (8), p.083502-083502-28
Main Authors: Baggett, L. W., Jorgensen, P. E. T., Merrill, K. D., Packer, J. A.
Format: Article
Language:English
Subjects:
ALGEBRA
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Exact sciences and technology
HILBERT SPACE
Mathematical methods in physics
Mathematics
MULTIPLICITY
Physics
RESOLUTION
Sciences and techniques of general use
VECTORS
WAVE FUNCTIONS
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Summary:We consider wavelets in L 2 ( R d ) which have generalized multiresolutions. This means that the initial resolution subspace V 0 in L 2 ( R d ) is not singly generated. As a result, the representation of the integer lattice Z d restricted to V 0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R d can be constructed directly from the generalized wavelet filters.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1982768