Fractals everywhere
Ten lectures on wavelets
Multiresolution analyses based on fractal functions
Journal of Approximation Theory
Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets
SIAM Journal on Mathematical Analysis
Arbitrarily smooth orthogonal nonseparable wavelets in R2
SIAM Journal on Mathematical Analysis
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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 continous 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 continous piecewise linear functions on a uniform subdivision of the original triangular lattice.