A time-frequency density criterion for operator identification

TL;DR

This paper introduces a necessary density criterion for identifying classes of Hilbert-Schmidt operators with time-frequency structure, extending Gabor frame density concepts to operator identification.

Contribution

It establishes a new density criterion for operator identifiability based on Gabor frame theory, with practical examples of identifiable classes.

Findings

Density criterion for operator identifiability established

Extension of Gabor frame density concepts to operators

Examples of identifiable operator classes provided

Abstract

We establish a necessary density criterion for the identifiability of time-frequency structured classes of Hilbert-Schmidt operators. The density condition is based on the density criterion for Gabor frames and Riesz bases in the space of square integrable functions. We complement our findings with examples of identifiable operator classes.