On Multivariate Splines, Matroids, and the Ext-Functor

Dahmen W, Dress A, Micchelli CA (1996)
Advances in Applied Mathematics 17(3): 251-307.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dahmen, Wolfgang; Dress, AndreasUniBi; Micchelli, Charles A.
Abstract / Bemerkung
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.
Erscheinungsjahr
1996
Zeitschriftentitel
Advances in Applied Mathematics
Band
17
Ausgabe
3
Seite(n)
251-307
ISSN
0196-8858
Page URI
https://pub.uni-bielefeld.de/record/1638645

Zitieren

Dahmen W, Dress A, Micchelli CA. On Multivariate Splines, Matroids, and the Ext-Functor. Advances in Applied Mathematics. 1996;17(3):251-307.
Dahmen, W., Dress, A., & Micchelli, C. A. (1996). On Multivariate Splines, Matroids, and the Ext-Functor. Advances in Applied Mathematics, 17(3), 251-307. https://doi.org/10.1006/aama.1996.0012
Dahmen, W., Dress, A., and Micchelli, C. A. (1996). On Multivariate Splines, Matroids, and the Ext-Functor. Advances in Applied Mathematics 17, 251-307.
Dahmen, W., Dress, A., & Micchelli, C.A., 1996. On Multivariate Splines, Matroids, and the Ext-Functor. Advances in Applied Mathematics, 17(3), p 251-307.
W. Dahmen, A. Dress, and C.A. Micchelli, “On Multivariate Splines, Matroids, and the Ext-Functor”, Advances in Applied Mathematics, vol. 17, 1996, pp. 251-307.
Dahmen, W., Dress, A., Micchelli, C.A.: On Multivariate Splines, Matroids, and the Ext-Functor. Advances in Applied Mathematics. 17, 251-307 (1996).
Dahmen, Wolfgang, Dress, Andreas, and Micchelli, Charles A. “On Multivariate Splines, Matroids, and the Ext-Functor”. Advances in Applied Mathematics 17.3 (1996): 251-307.

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