Finite Sensor Dynamical Sampling

CABRELLI, CARLOS A.; MOLTER, URSULA M.; PHILIPP, FRIEDRICH; PATERNOSTRO, VICTORIA

Tallin

Congreso; 12th International Conference on Sampling Theory and Applications, SampTA 2017; 2017

SAMPTA

Dynamical Sampling aims to subsample solutions of linear dynamical systems at various times. One way to model this consists of considering inner products of the form $\$, where $h$ is the signal, $(f_i)$ a system of fixed vectors and $A$ a linear operator which is connected with the dynamical system. Here, we characterize those systems $(A^nf_i)_{n\in\N,\,i\in I}$ with finite index sets $I$ and normal operators $A$ which are frames for the underlying Hilbert space. It turns out that this problem is intimately connected with spectral properties of the operator $A$ and complex analysis in the unit disk. We also provide conditions on the spectral properties of $A^*$ for non-normal $A$.