Wiener's tauberian theorem for spherical functions on the automorphism group of the unit disk

Yaakov Ben Natan, Yoav Benyamini, Håkan Hedenmalm, Yitzhak Weit

Research output: Contribution to journalArticlepeer-review

Abstract

Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the convolution algebra of spherical integrable functions on the (conformal) automorphism group of the unit disk to be dense, or to have as closure the closed ideal of functions with integral 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 Agranovskiǐ).

Original languageEnglish
Pages (from-to)199-224
Number of pages26
JournalArkiv for Matematik
Volume34
Issue number2
DOIs
StatePublished - Oct 1996

ASJC Scopus subject areas

  • General Mathematics

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