How Many Holes Can Locally Linearly Independent Reenable Function Vectors Have?

In this paper we consider the support properties of locally linearly independent re nable function vectors r T We propose an algorithm for computing the global support of the components of Further for T we investigate the supports especially the possibility of holes of re nable function vectors if local linear independence is assumed Finally we give some necessary conditions for local linear independence in terms of rank conditions for special matrices given by the re nement mask But we are not able to give a nal answer to the question whether a locally linearly independent function vector can have more than one hole Introduction Let r T r IN be a vector of compactly supported continuous functions on IR The function vector is said to be re nable if it satis es a vector re nement equation x X