frame operator

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Loyford Njagi, Bernard Nzimbi, Moindi S. "A note on analysis and synthesis operators of a frame and reconstruction of a signal from frame coefficients." International Journal of Statistics and Applied Mathematics. 2019;4(5):93-99. AbstractWebsite

We discuss basic properties of Analysis and synthesis operators a frame. The structure of matrix
representation of the Synthesis operator is also analysed. This matrix is what most frame constructions in
fact focus on. The frame operator which is just the joining together of the analysis and synthesis
operators is fundamental for the reconstruction of signals from frame coefficients

Njagi L, Nzimbi BM, Moindi SK. "On Pseudo-inverses and Duality of Frames in Hilbert Spaces." International Journal of Mathematics and its Applications (IJMAA). 2019;7(2):75-88. AbstractWebsite

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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