Universal Nonuniform Sampling of Positive Operator Orbits via Complete Stein--Pick Criteria and Density

We study nonuniform sampling for positive operator systems. Given a locally finite set \(T\subset[0,\infty)\), we determine when exact observability of \(\{CA^n\}_{n\in\mathbb N}\) implies exact observability of \(\{CA^t\}_{t\in T}\) for every positive operator \(A\) and every observation operator \