Interpolating and sampling sequences for entire functions

Nicolas Marco, Xavier Massaneda, Joaquim Ortega-Cerdà

    Research output: Contribution to journalArticleResearchpeer-review

    47 Citations (Scopus)

    Abstract

    We characterise interpolating and sampling sequences for the spaces of entire functions f such that fe-φ ε LP(C), p ≥ 1, where φ 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 δ. They generalise previous results by Seip for the case φ(z) = |z|2, Berndtsson and Ortega-Cerdà and Ortega-Cerdà and Seip for the case when δ is bounded above and below, and Lyubarskiǐ and Seip for 1-homogeneous weights of the form φ(z) = |z|h(arg z), where h is a trigonometrically strictly convex function.
    Original languageEnglish
    Pages (from-to)862-914
    JournalGeometric and Functional Analysis
    Volume13
    Issue number4
    DOIs
    Publication statusPublished - 13 Oct 2003

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