Abstract
We consider the space Sn=Sn(v0,…,vn+r) of compactly supported Cn−1 piecewise polynomials on a mesh M of lines through ℤ2 in directions v0,…,vn+r. A sequence ψ=(ψ1,…,ψr) of elements of Sn is called a multi-box spline if every element of Sn is a finite linear combination of shifts of (the components of) ψ. For the case n=2, 3 we give some examples for multi-box splines and show that they are not always stable. It is further shown that any Cn−1 piecewise polynomial of degree n≥2 on M, is possibly a symmetric multi-box spline.
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