# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "Permissible and defective support patterns of covariance matrices in the identification of stochastic operators"

#### Pohl, Volker

This contribution studies support patterns of covariance matrices appearing in the problem of identifying stochastic operators. The identification problem reduces to solving a linear system of equations associated with a measurement matrix having the form $G_{c} \otimes G_{c}$ with a Gabor matrix $G_{c}$ generated by a window $c$. We investigate support patterns of the object vector which allow the existence of a window $c$ that renders the linear system of equations to be solvable. Several classes of permissible patterns are presented and it is shown how the corresponding window vector needs to be chosen. It is also shown that there exist support patterns for which no window generates a solvable linear system of equations.

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