Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice

Details Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice

2011-02-21

arxiv.org/abs/1102.4246v1

Mathematics

Numerical Analysis

34 pages, 6 figures

Scientific paper

We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\tau$-integers where $\tau$ is the golden-mean. The resulting spaces then generate a multiresolution analysis of $L^2(\mathbf{R})$ with scaling factor $\tau$.

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