Compactly Supported Powell–Sabin Spline Multiwavelets in Sobolev Spaces
نویسندگان
چکیده
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 H(R), and we find that 0.431898 < s < 5/2. For those s, discretizations of H -elliptic problems with respect to the wavelet basis lead to uniformly well-conditioned stiffness matrices, resulting in an asymptotically optimal preconditioning method.
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