Abstract
Abstract : Local support bases for piecewise polynomial spaces are important for applications such as finite element methods, data fitting etc. In (BH sub 1) a general construction principle for such B-splines was described. A special case are the so called box-splines. They have a particularly regular discontinuity pattern and coincide in special cases with standard finite elements. It is hoped that using translates of box-splines will lead, at least in two variables, to a unified theory for piecewise polynomial functions on regular meshes. This note is a first attempt in this direction and deals with basic approximation properties of translates of one box-splines such as stability, degree of approximation etc. (Author)
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