Powell-Sabin spline prewavelets on the hexagonal lattice

In this paper we give an explicit construction of compactly supported wavelets on differentiable, twodimensional, piecewise polynomial quadratic finite element spaces of L²(R²), sampled on the hexagonal grid. The obtained prewavelet basis is stable in the Sobolev spaces H^s for |s| < 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 2π/3.series: Applied Harmonic Analysisstatus: publishe