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Bounds on the dimension of spaces of multivariate piecewise polynomials. (English) Zbl 0601.41034
In 1979 [Multivariate approximation theory, Proc. Conf. Math. Res. Inst. Oberwolfach, 1979, ISNM Vol. 51, 396-412 (1979; Zbl 0461.41006)] the author gave a lower bound on the dimension of spaces of piecewise polynomials defined on a triangulation. In this paper both lower and upper bounds for general rectilinear partitions are presented. The results obtained are illustrated by many examples.

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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