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Nontensor product wavelet packets in \(L_ 2 (\mathbb{R}^ s)\). (English) Zbl 0826.42025

Summary: R. R. Coifman and Y. Meyer [Orthonormal wavelet packet bases (preprint)], constructed univariate and tensor product bivariate orthonormal wavelet packets. In this note, we give a general way to construct nontensor product orthonormal multivariate wavelet packets with an exponential decay. In particular, we give concrete constructions of exponentially decaying orthonormal wavelet packets and compactly supported semiorthogonal wavelet packets of two and three variables directly from the scaling function and its refinement mask.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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