In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, which 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–Pólya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling.
Bernstein Spaces on Siegel CR Manifolds / M. Calzi, M.M. Peloso. - In: ANALYSIS AND MATHEMATICAL PHYSICS. - ISSN 1664-2368. - 12:5(2022), pp. 123.1-123.33. [10.1007/s13324-022-00733-2]
Bernstein Spaces on Siegel CR Manifolds
M. Calzi
Primo
;M.M. PelosoUltimo
2022
Abstract
In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, which 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–Pólya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling.
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