Maximum Robustness and Surgery of Frames in finite dimensions

Abstract

We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and surgery of frames. We also answer the question of when length surgery resulting in a tight frame set for Hn is possible.

This work was done as a part of the REU program in Summer 2011. Submitted