Weighted and controlled frames were introduced to speed up the inversion algorithm for the frame matrix of a wavelet frame. In this project, these kinds of frames are investigated further.
The frame multiplier concept is closely linked to the weighted frames concept. The frame operator of the weighted frame is simply a frame multiplier of the original frame. This project aims to explore this synergy. Finding an efficient way to invert the frame operator by applying weights to a given frame would be especially interesting. Weights are searched, for which the frame bounds are as "tight" as possible, meaning the spectrum is more concentrated. The first numerical experiments to find optimal weights have been conducted.
Weighted frames have already been applied to wavelets on the sphere. Also, the original work by Duffin and Schaefer dealt with the problem of finding such weights for a sequence of exponentials.
- J. P. Antoine, Unité de physique théorique et de physique mathématique – FYMA