Interpolating and sampling sequences for entire functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2003Embargo end date: 01 Jan 2002Publisher:Springer Science and Business Media LLCJournal:Geometric And Functional Analysis, volume 13, pages 862-914 (issn: 1016-443X, eissn: 1420-8970,

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Authors: Marco, Nicolás; Massaneda Clares, Francesc Xavier; Ortega Cerdà, Joaquim;

doi: 10.1007/s00039-003-0434-7 , 10.48550/arxiv.math/0205241

arXiv: math/0205241

handle: 2445/164726

Interpolating and sampling sequences for entire functions

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Abstract

We characterise interpolating and sampling sequences for the spaces of entire functions f such that f e^{-phi} belongs to L^p(C), p>=1 (and some related weighted classes), 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 the Laplacian of phi. They generalise previous results by Seip for the case phi(z)=|z|^2, and by Berndtsson & Ortega-Cerd�� and Ortega-Cerd�� & Seip for the case when the Laplacian of phi is bounded above and below.

Related Organizations

University of Barcelona
Spain
Autonomous University of Barcelona
Spain

Keywords

Functional analysis, Mathematics - Complex Variables, Stochastic integrals, Funcions de variables complexes, Quasi-analytic and other classes of functions of one complex variable, Hilbert space, Interpolation, Functions of complex variables, 30E05; 46E20, Funcions analítiques, Interpolació (Matemàtica), Espais de Hilbert, Banach spaces of continuous, differentiable or analytic functions, Anàlisi funcional, Analytic functions, 30E05, FOS: Mathematics, Complex Variables (math.CV), 46E20

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