FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1939-1950.

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

李登峰¹, 李艳婷²

1 School of Mathematics and Computer, Wuhan Textile University, Wuhan 430200, China;
2 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China

收稿日期:2017-03-13 修回日期:2018-05-28 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Dengfeng LI E-mail:dfli2003@aliyun.com
作者简介:Yanting LI,E-mail:ytli1227@126.com
基金资助:
This work was partially supported by the National Natural Science Foundation of China (61471410).

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

Dengfeng LI¹, Yanting LI²

1 School of Mathematics and Computer, Wuhan Textile University, Wuhan 430200, China;
2 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China

Received:2017-03-13 Revised:2018-05-28 Online:2018-12-25 Published:2018-12-28
Contact: Dengfeng LI E-mail:dfli2003@aliyun.com
Supported by:
This work was partially supported by the National Natural Science Foundation of China (61471410).

摘要/Abstract

摘要： The objective of this paper is to investigate the question of modifying a given generalized Bessel sequence to yield a generalized frame or a tight generalized frame by finite extension. Some necessary and sufficient conditions for the finite extensions of generalized Bessel sequences to generalized frames or tight generalized frames are provided, and every result is illustrated by the corresponding example.

关键词: frame, generalized frame, generalized Bessel sequence

Abstract: The objective of this paper is to investigate the question of modifying a given generalized Bessel sequence to yield a generalized frame or a tight generalized frame by finite extension. Some necessary and sufficient conditions for the finite extensions of generalized Bessel sequences to generalized frames or tight generalized frames are provided, and every result is illustrated by the corresponding example.

Key words: frame, generalized frame, generalized Bessel sequence

李登峰, 李艳婷. FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES[J]. 数学物理学报(英文版), 2018, 38(6): 1939-1950.

Dengfeng LI, Yanting LI. FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1939-1950.

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FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

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