On Finite Dimensional Hilbert Space Frames, Dual and Normalized Frames and Pseudo-inverse of the Frame Operator

Authors

  • L. Njagi Department of Mathematics, Meru University of Science and Technology, P.O. Box 972-60200,Meru
  • B. M. Nzimbi School of Mathematics, University of Nairobi, Chiromo Campus, P. O. Box 30197-00100, Nairobi
  • S. K. Moindi School of Mathematics, University of Nairobi, Chiromo Campus, P. O. Box 30197-00100, Nairobi

DOI:

https://doi.org/10.53555/nnms.v5i11.528

Keywords:

Hilbert space, frame, Dual frame, Psuedo-inverse, Normalized

Abstract

In this research paper we do an introduction to Hilbert space frames. We also discuss various frames in the Hilbert space. A frame is a generalization of a basis. It is useful, for example, in signal processing. It also allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its frame coe?cients. Our focus will be on frames in ?nite dimensional spaces.

References

1. A wavelet tour of signal processing: the sparse way, Stephane Mallat, Elsevier, M A, 2009. 2. Ten lectures on wavelet, Ingrid Daubechies, Springer- Verlag,1992.
3. “Finite Normalized Tight Frames”, Benedetto & Fickus, Advances in Computational Mathematics 18:357-385, 2003

Published

2018-11-30

How to Cite

Njagi, L., Nzimbi, B. M., & Moindi, S. K. (2018). On Finite Dimensional Hilbert Space Frames, Dual and Normalized Frames and Pseudo-inverse of the Frame Operator. Journal of Advance Research in Mathematics And Statistics, 5(11), 01–10. https://doi.org/10.53555/nnms.v5i11.528