The shift-invariant subspaces in L1(R)1

Authors:
Wu Zhengchang
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China
Venue:
Journal of Approximation Theory
Year:
2002

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Abstract

In this paper, we investigate finitely generated shift-invariant subspaces in L1 (R). We first introduce the notion of the convolution of a vector sequence and a matrix sequence. Then by the theory of dual space of the normed linear space we obtain the complete characterizations of finitely generated shift-invariant spaces in L1 (R), based on the existence of generator with linearly independent shifts in finitely generated shift-invariant subspaces on the real line.