Bernstein Spaces on Siegel CR Manifolds

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-Pólya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling.

arXiv comment22 pages, no figures

References in corpus (6)

• Real Paley-Wiener theorems and local spectral radius formulas
• Density of Sampling and Interpolation in Reproducing Kernel Hilbert Spaces
• Carleson and reverse Carleson measures on homogeneous Siegel domains
• Toeplitz and Cesàro-Type Operators on Homogeneous Siegel Domains
• Bernstein Spaces on Siegel CR Manifolds
• Sampling in spaces of entire functions of exponential type in ${\mathbb{C}}^{n+1}$

Cited by in corpus (5)

• Bernstein Spaces on Siegel CR Manifolds
• Boundedness of Bergman projectors on homogeneous Siegel domains
• Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds
• Paley-Wiener-Schwartz Theorems on Quadratic CR Manifolds
• On the Theory of Bergman Spaces on Homogeneous Siegel Domains