Compactly supported Powell-Sabin spline multiwavelets in Sobolev spaces
Jan Maes, Adhemar Bultheel · Lirias · 2005
In this paper we construct Powell--Sabin spline multiwavelets on the hexagonal lattice in a shift-invariant setting. This allows us to use Fourier techniques to study the range of the smoothness parameter s for which the wavelet basis is a Riesz basis in the Sobolev space Hs(R²) and we find that 0.360704 < s < 5/2. For those s, discretizations of Hs-elliptic problems with respect to the wavelet basis lead to uniformly well-conditioned stiffness matrices, resulting in an asymptotically optimal preconditioning method.