Interpolation by periods in a planar domain

    Research output


    Let Ω ⊂ ℝ2 be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L2(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ2 \ Ω. For which Ω the collection of such period sequences coincides with ℓ2 We give an answer in terms of metric properties of holes in Ω.

    Translated title of the contributionИнтерполяция по периодам в плоской области
    Original languageEnglish
    Pages (from-to)597-669
    Number of pages73
    JournalSt. Petersburg Mathematical Journal
    Issue number5
    Publication statusPublished - 1 Jan 2017

    Scopus subject areas

    • Analysis
    • Geometry and Topology

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