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 language | English |
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Pages (from-to) | 199-224 |
Number of pages | 26 |
Journal | Arkiv for Matematik |
Volume | 34 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1996 |
ASJC Scopus subject areas
- General Mathematics