Research PaperNo Access

A class of vector-valued subspace weak Gabor duals of type II

Jing Zhao

College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China

E-mail Address: jingzhao@emails.bjut.edu.cn

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and

Yun-Zhang Li

College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China

E-mail Address: yzlee@bjut.edu.cn

Corresponding author.

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https://doi.org/10.1142/S021969131850056XCited by:3 (Source: Crossref)

Abstract

The theory of vector-valued frames (also called superframes) has important applications in signal multiplexing, and has interested many mathematicians in recent years. In this paper, we introduce the notion of weak Gabor duals of type II under the setting of subspaces $L^{2} (S, ℂ^{L})$ , where $S$ is a periodic subset of $ℝ$ . Using the Zak transform matrix method, we characterize weak Gabor duals of type II and their uniqueness. An example is also presented to illustrate the generality of our results.

Keywords:

AMSC: 42C40, 42C15

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