Robustness and Surgery of Frames

We characterize frames in ℝⁿ that are robust to k erasures. The characterization is given in terms of the support of the null space of the synthesis operator of the frame. A necessary and sufficient condition is given for when an (r, k)-surgery on unit-norm tight frames in R2 are possible. Also a generalization of a known characterization of the existence of tight frames with prescribed norms is given.