Quantitative Estimates of Sampling Constants in Model Spaces

We establish quantitative estimates for sampling (dominating) sets in model spaces associated with meromorphic inner functions, i.e., those corresponding to de Branges spaces. Our results encompass the Logvinenko-Sereda-Panejah (LSP) Theorem including Kovrijkine's optimal sampling constants for Paley-Wiener spaces. It also extends Dyakonov's LSP theorem for model spaces associated with bounded derivative inner functions. Considering meromorphic inner functions allows us to introduce a new geometric density condition, which is sufficient for sampling sets in general and also necessary when the inner function is one component. This, in comparison to Volberg's characterization of sampling measures in terms of harmonic measure, enables us to obtain explicit estimates on the sampling constants. The methods combine Baranov-Bernstein inequalities, reverse Carleson measures and Remez inequalities.