CHALMOUKIS, Nikolaos; HARTMANN, Andreas; KELLAY, Karim; WICK, Brett

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CHALMOUKIS, Nikolaos
Dipartimento di Matematica

HARTMANN, Andreas
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

international mathematical research notices. 2022, vol. 17, p. 13629-13658

Résumé en anglais

We discuss random interpolation in weighted Dirichlet spaces $\mathcal{D}_\alpha$, $0\leq \alpha\leq 1$. While conditions for deterministic interpolation in these spaces depend on capacities which are very hard to estimate in general, we show that random interpolation is driven by surprisingly simple distribution conditions. As a consequence, we obtain a breakpoint at $\alpha=1/2$ in the behavior of these random interpolatingsequences showing more precisely that almost sure interpolating sequences for $\mathcal{D}_\alpha$ are exactly the almost sure separated sequences when $0\le \alpha<1/2$ (which includes the Hardy space $H^2=\mathcal{D}_0$), and they are exactly the almost sure zero sequences for $\mathcal{D}_\alpha$ when $1/2 \leq \alpha\le 1$ (which includes the classical Dirichlet space $\mathcal{D}=\mathcal{D}_1$).< Réduire

Mots clés en anglais

random sequences

Carleson measure

Interpolating sequences

separation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191830

Project ANR

Noyaux reproduisants en Analyse et au-delà - ANR-18-CE40-0035

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251