PUB - Publikationen an der Universität Bielefeld

Various important issues in the theory of multivariate splines lead to the following problem. Given some family of commuting endomorphisms L(x), x is an element of X, on some vector space L, determine the dimension of the intersection of null spaces of certain products Pi(upsilon is an element of V) L(u)psilon(lambda upsilon), V subset of X, of these endomorphisms. In this paper we reinterpret such problems in the general framework of homological algebra. This allows us not only to rederive the results by Dahmen and Micchelli (Adv. in Math. 76, 1989, 33-93), as well as some related recent results by de Boor and Ron, Shen, Jia, and Riemenschneider, but also to extend them in various directions that are not accessible by the techniques employed in these papers. (C) 1996 Academic Press, Inc.