Quantitative estimates of sampling constants in model spaces
Idioma
en
Article de revue
Este ítem está publicado en
American Journal of Mathematics. 2020, vol. 142, n° 4, p. 1301-1326
Johns Hopkins University Press
Resumen en inglés
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 ...Leer más >
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 .< Leer menos
Palabras clave en inglés
Model space
Bernstein inequalities
sampling
reverse Carleson measure
Proyecto ANR
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Orígen
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