Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1939-1950.

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FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

Dengfeng LI1, Yanting LI2   

  1. 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).

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

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