On the linear independence of multivariate b-splines. Complete configurations

The first part of this paper is concerned with global characterizations of both the multivariate ß-spline and the multivariate truncated power function as smooth piecewise polynomials. In the second part of the paper we establish combinatorial criteria for the linear independence of multivariate ß-splines corresponding to certain configurations of knot sets. © 1983 American Mathematical Society.