A Construction of Compactly Supported Biorthogonal Scaling Vectors and Multiwavelets on R2 Original Research Article

In Kessler (Appl. Comput. Harmonic Anal.9 (2000), 146–165), a construction was given for a class of orthogonal compactly supported scaling vectors on R2, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the original triangular lattice.