2007 | OriginalPaper | Buchkapitel
Powell-Sabin Spline Prewavelets on the Hexagonal Lattice
verfasst von : Jan Maes, Adhemar Bultheel
Erschienen in: Wavelet Analysis and Applications
Verlag: Birkhäuser Basel
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In this paper we give an explicit construction of compactly supported prewavelets on differentiable, twodimensional, piecewise polynomial quadratic finite element spaces of
L
2
(ℝ
2
), sampled on the hexagonal grid. The obtained prewavelet basis is stable in the Sobolev spaces
$$ \mathcal{H}^s $$
for
$$ |s| < \tfrac{5} {2} $$
. In particular, the prewavelet basis is generated by one single function vector
ψ
consisting of three generating functions
ψ
1
,
ψ
2
,
ψ
3
that are globally invariant by a rotation of 2
π
/3.