Research PaperNo Access

Partial Gabor frames and dual frames

Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, P. R. China

E-mail Address: yutian@zzuli.edu.cn

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Hui-Fang Jia

School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030001, P. R. China

E-mail Address: jiahuifang@sxu.edu.cn

Corresponding author.

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, and

Guo-Liang He

Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, P. R. China

E-mail Address: glhemath@163.com

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https://doi.org/10.1142/S0219691321500351Cited by:1 (Source: Crossref)

Abstract

The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.

Keywords:

AMSC: 42C40, 42C15

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