A.E. convergence of spectral sums on lie groups

Christopher Meaney*, Detlef Müller, Elena Prestini

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    Let £ be a right-invariant sub-Laplacian on a connected Lie group G, and let SRf := f dEλf, R ≥ O, denote the associated "spherical partial sums," where £ = ∫0 λ dEλ is the spectral resolution of £. We prove that SRf(x) converges a.e. to f(x) as R → ∞ under the assumption log(2 + C) f ∞ L 2 (G).

    Original languageEnglish
    Pages (from-to)1509-1520
    Number of pages12
    JournalAnnales de l'Institut Fourier
    Volume57
    Issue number5
    Publication statusPublished - 2007

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