Minimal generator sets for finitely generated shift - invariant subspaces of L 2 ( R n ) ✩
نویسندگان
چکیده
Let S be a shift-invariant subspace of L2(Rn) defined by N generators and suppose that its length L, the minimal number of generators of S, is smaller than N . Then we show that at least one reduced family of generators can always be obtained by a linear combination of the original generators, without using translations. In fact, we prove that almost every such combination yields a new generator set. On the other hand, we construct an example where any rational linear combination fails. 2005 Elsevier Inc. All rights reserved.
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