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 Lp$L<^>p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.
Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds / M. Calzi, M.M. Peloso. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - (2023), pp. 1-34. [Epub ahead of print] [10.1002/mana.202200058]
Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds
M. Calzi
Primo
;M.M. PelosoUltimo
2023
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 Lp$L<^>p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.Pubblicazioni consigliate
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