ON FINITE DIMENSIONAL HILBERT SPACE FRAMES, DUAL AND NORMALIZED FRAMES AND PSEUDO- INVERSE OF THE FRAME OPERATOR
DOI:
https://doi.org/10.53555/nnms.v5i11.528Keywords:
Hilbert space, frame, Dual frame, Psuedo-inverse, Normalized framesAbstract
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 coefficients. Our focus will be on frames in finite dimensional spaces.
References
A Wavelet Tour of Signal Processing, Stephane Mallat
Ten Lectures on Wavelets, Ingrid Daubechies
“Finite Normalized Tight Frames”, Benedetto & Fickus, Advances in Computational Mathematics 18:357-385, 2003
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