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On Multivariate Splines, Matroids, and the Ext-Functor

✍ Scribed by Wolfgang Dahmen; Andreas Dress; Charles A. Micchelli

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 499 KB
Volume: 17
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0012

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✦ Synopsis

Various important issues in the theory of multivariate splines lead to the following problem. Given some family of commuting endomorphisms L , x g X, x on some vector space S S , determine the dimension of the intersection of null spaces of certain products Ł L ¨, V ; X, of these endomorphisms. In this ¨g V 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 Ž . Ad¨. 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.

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