Interpolating and sampling sequences for entire functions

By N. Marco, X. Massaneda, J. Ortega‐Cerdà. 2002

105 citations recorded by the source corpus.

AbstractWe characterise interpolating and sampling sequences for the spaces of entire functions f such that $ f e^{-\phi}\in L^p(\C)$, $p\geq 1 $, where $\phi$ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by $\Delta\phi$. They generalise previous results by Seip for the case $\phi(z)=|z|^2$, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip for the case when $\Delta\phi$ is bounded above and below, and Lyubarskiĭ and Seip for 1-homogeneous weights of the form $\phi(z)=|z|h(\arg z)$, where h is a trigonometrically strictly convex function.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/78a63eb0acd6d0a6fef1a434d5c4a7aef5f1b687

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In Applied Mathematics

Citations in the corpus

Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces (2013, background): “Indeed, the family of test functions considered to study the boundedness of Tg on these spaces is basically the one introduced in [8] to characterize sampling and interpolation sequences (such problems for Fock spaces with nonradial weights e−φ where ∆φ is a doubling measure were considered in [15])”
Boundedness of the Bergman projection on $L^p$ spaces with exponential weights (2013, unknown): “The function ρ−2 can be regarded as a regularized version of ∆φ (see [10]).”
Compactness of the solution operator to ∂¯ in weighted L2-spaces☆ (2007, unknown): “In fact Marco, Massaneda and Ortega-Cerda [ MMO ] (Theorem C, p. 884) found out that already condition (1) in the last definition implies that the canonical solution operator to ∂ is continuous.”
Sampling and interpolation in large Bergman and Fock spaces (2007, background): “Ortega-Cerdà [18] described sampling and interpolation sets for the Fock spaces Aph(C) for a wide class of h such that h is a doubling measure.”
Pointwise Estimates for the Bergman Kernel of the Weighted Fock Space (2008, methodology): “2 Preliminaires In this section we collect some material from [3] and [12] that will be used along the proofs and we deduce some easy estimates for the Bergman kernel near the diagonal.”