On Pseudo-inverses and Duality of Frames in Hilbert Spaces


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Authors

  • L. Njagi Department of Mathematics, School of Pure and Applied Sciences, Meru University of Science and Technology, Meru, Kenya
  • B. M. Nzimbi School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
  • S. K. Moindi School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya

Keywords:

Frame, dual frame, tight frame, canonical tight frame, Parseval, frame operator, analysis operator, Grammian

Abstract

In this paper, we show how to find dual frames using the notion of singular value decomposition and pseudo-inverses of an operator in a Hilbert space. We will also show how properties of dual frames are linked to the spectral properties of the dual frame operator and the Grammian.

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Published

15-06-2019

How to Cite

L. Njagi, B. M. Nzimbi, & S. K. Moindi. (2019). On Pseudo-inverses and Duality of Frames in Hilbert Spaces. International Journal of Mathematics And Its Applications, 7(2), 75–88. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/250

Issue

Vol. 7 No. 2 (2019)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.