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 theoremfor model spaces associated with bounded derivative inner functions. Considering meromorphic inner functions allows us tointroduce a new geometric density condition, in terms of which the sampling sets are completely characterized. This, incomparison to Volberg's characterization of sampling measures in terms of harmonic measure, enables us to obtain explicitestimates on the sampling constants. The methods combine Baranov-Bernstein inequalities, reverse Carleson measures andRemez inequalities .

中文翻译：

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模型空间中采样常数的定量估计

我们为与亚纯内函数相关的模型空间中的采样（支配）集建立定量估计，即对应于 de Branges 空间的那些。我们的结果包含 Logvinenko-Sereda-Panejah (LSP) 定理，包括 Kovrijkine 对 Paley-Wiener 空间的最佳采样常数。它还扩展了 Dyakonov 的 LSP 定理，用于与有界导数内函数相关的模型空间。考虑亚纯内函数允许我们引入新的几何密度条件，根据该条件可以完全表征采样集。这与沃尔伯格在谐波测量方面对采样测量的表征相比，使我们能够获得对采样常数的明确估计。这些方法结合了 Baranov-Bernstein 不等式，