The Shift-Invariant Subspaces in L1(R) Original Research Article

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.