Abstract
In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, 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.
Disciplines
Analysis | Applied Mathematics
Recommended Repository Citation
Kessler, Bruce. (2001). A Construction of Compactly-Supported Biorthogonal Scaling Vectors and Multiwavelets on $R^2$. Journal of Approximation Theory, 117 (2), 229-254.
Available at:
https://digitalcommons.wku.edu/math_fac_pub/1
Comments
Published by Journal of Approximation Theory, 117 (2) (August 2002): 229-254. Copyright 2002, Elsevier Inc. All rights reserved. This version posted with permission as author's final version.