Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 31, Issue 4, Pages 726-739Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036141097323333
Keywords
frame; wavelet; wavelet frame; Riesz basis; shift-invariant space
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This paper presents a detailed analysis of the splitting trick which splits, for example, the half-shifts of a function into the shifts of two functions. When a Riesz basis of a shift-invariant subspace is split, the optimal bounds of the resulting Riesz basis are obtained. Most importantly, by the splitting trick we built wavelet frame packets as orthogonal wavelet packets constructed by Coifman and Meyer. Their algorithms for finding best basis for a function also apply to our setting.
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