Maximum Robustness and Surgery of Frames in finite dimensions

TL;DR

This paper investigates the robustness of frames in finite-dimensional Hilbert spaces, providing methods to determine maximum robustness, analyzing tight subframes, and exploring conditions for frame surgery to produce tight frames.

Contribution

It introduces a new method to compute maximum robustness of frames and characterizes when frame surgery can yield tight frames in finite dimensions.

Findings

Method to determine maximum robustness of frames

Results on tight subframes and their properties

Conditions under which frame surgery produces tight frames

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.