HARTMANN, Andreas; JAMING, Philippe; KELLAY, Karim

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HARTMANN, Andreas
Institut de Mathématiques de Bordeaux [IMB]

JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

KELLAY, Karim
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

American Journal of Mathematics. 2020, vol. 142, n° 4, p. 1301-1326

Johns Hopkins University Press

Résumé en anglais

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 .< Réduire

Mots clés en anglais

Model space

Bernstein inequalities

sampling

reverse Carleson measure

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193623

Project ANR

Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251