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Bessel Sequences and Its F-Scalability

Published online by Cambridge University Press:  29 May 2015

Lei Liu
Affiliation:
Department of Mathematics, Shantou University, Shantou 515063, China
Xianwei Zheng*
Affiliation:
Department of Mathematics, Shantou University, Shantou 515063, China
Jingwen Yan
Affiliation:
Guangdong Provincial Key Laboratory of Digital Signal and Image Processing Techniques, Shantou University, Shantou 515063, China
Xiaodong Niu
Affiliation:
College of Engineering, Shantou University, Shantou 515063, China
*
*Corresponding author. Email: wliulei@stu.edu.cn (L. Liu), 09xwzheng@stu.edu.cn (X. Zheng), jwyan@stu.edu.cn (J. Yan), xdniu@stu.edu.cn (X. Niu)
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Abstract

Frame theory, which contains wavelet analysis and Gabor analysis, has become a powerful tool for many applications of mathematics, engineering and quantum mechanics. The study of extension principles of Bessel sequences to frames is important in frame theory. This paper studies transformations on Bessel sequences to generate frames and Riesz bases in terms of operators and scalability. Some characterizations of operators that mapping Bessel sequences to frames and Riesz bases are given. We introduce the definitions of F-scalable and P-scalable Bessel sequences. F-scalability and P-scalability of Bessel sequences are discussed in this paper, then characterizations of scalings of F-scalable or P-scalable Bessel sequences are established. Finally, a perturbation result on F-scalable Bessel sequences is derived.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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