Pseudoaffinity de Boor algorithm and blossoms

Authors: MarieLaurence Mazure

Publish Date: 2006/12/06

Volume: 26, Issue: 1-3, Pages: 305-322

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Abstract

In order to ensure existence of a de Boor algorithm hence of a Bspline basis in a given spline space with n+1dimensional sections it is important to be able to generate each spline by restriction to the diagonal of a symmetric function of n variables supposed to be pseudoaffine wr to each variable We proved that a way to obtain these three properties symmetry npseudoaffinity diagonal property is to suppose the existence of blossoms on the set of admissible ntuples given that blossoms are defined in a geometric way by means of intersections of osculating flats In the present paper we examine the converse do symmetry npseudoaffinity and diagonal property imply existence of blossomsI would like to make a present of this article to Mariano Gasca to celebrate many fruitful years of research and above all this his 60th birthday I would also like to thank him for his permanent cheerfulness and simplicity of nature which have made each encounter with him a pleasure to be looked forward to

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