The Shift-Invariant Subspaces in L₁(R)

Author: Zhengchang W.

Source: Journal of Approximation Theory, Volume 118, Number 1, September 2002 , pp. 81-93(13)

Publisher: Academic Press

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. © 2002 Elsevier Science (USA).

Keywords: shift-invariant spaces; linearly independent shifts; generator; annihilator.

Language: English

Document Type: Research article

DOI: http://dx.doi.org/10.1006/jath.2002.3711

Affiliations: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, People's Republic of China

Publication date: 2002-09-01

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• In this Subject: Mathematics and Statistics
• By this author: Zhengchang W.

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