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arXiv · 2112.07994

Bernstein Spaces on Siegel CR Manifolds

Mattia Calzi·Marco M. Peloso
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Abstract

In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, that we call Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to a given Siegel CR submanifold are $L^p$-integrable with respect to a natural measure. For these spaces, among other results, we prove the Plancherel-P\'olya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling.

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Mattia Calzi, Marco M. Peloso. 2021-12-15. Bernstein Spaces on Siegel CR Manifolds. https://doi.org/10.1007/s13324-022-00733-2

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