Wiener’s tauberian theorem in L1(G//k) and harmonic functions in the unit disk

Y. Ben Natan, Y. Benyamini, H. Hedenmalm, Y. Weit

Research output: Contribution to journalComment/Debate

Abstract

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in L1(G//K), the space of radial integrable functions on G = SU (1, 1), so that I = L1(G//K) or (Equation presented)—the ideal of L1(G//K) functions whose integral is zero. This is then used to prove a generalization of Furstenberg’s theorem which characterizes harmonic functions on the unit disk by a mean value property and a “two circles” Morera type theorem (earlier announced by Agranovskii).

Original languageEnglish
Pages (from-to)43-49
Number of pages7
JournalBulletin of the American Mathematical Society
Volume32
Issue number1
DOIs
StatePublished - Jan 1995

Keywords

  • Resolvent transform
  • Spectral synthesis
  • Spherical functions
  • SU(1, 1)
  • Two circles theorems
  • Wiener’s theorem
  • μ-harmonic functions

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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