Sums of matrix-valued wave packet frames in (L^2(ℝ^d,ℂ^{stimes r}))

The purpose of this paper is to first show relations between wave packet frame bounds and the scalars associated with finite sum of matrix-valued wave packet frames for the matrix-valued function space (L^2(ℝ^d, ℂ^{stimes r}). A sufficient condition with explicit wave packet frame bounds for finite sum of matrix-valued wave packet frames in terms of scalars and frame bounds associated with the finite sum of frames is given. An optimal estimate of wave packet frame bounds for the finite sum of matrix-valued wave packet frames is presented. In the second part, we show that the rate of convergence of the frame algorithm can be increased by using frame bounds and scalars associated with the finite sum of frames. Finally, a necessary and sufficient condition for finite sum of matrix-valued wave packet frames in terms of series associated with wave packet vectors is given