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arXiv · 2202.03752

Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Mattia Calzi·Marco M. Peloso
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Abstract

In this paper we introduce and study Carleson and sampling measures on Bernstein spaces on a class of quadratic CR manifold called Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to the given Siegel CR manifold are $L^p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficients conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.

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Mattia Calzi, Marco M. Peloso. 2022-02-08. Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds. https://doi.org/10.1002/mana.202200058

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