Abstract
Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal I in L^{1}(G//K), the space of radial integrable functions on G = SU (1, 1), so that I = L^{1}(G//K) or (Equation presented)—the ideal of L^{1}(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 language  English 

Pages (fromto)  4349 
Number of pages  7 
Journal  Bulletin of the American Mathematical Society 
Volume  32 
Issue number  1 
DOIs 

State  Published  Jan 1995 
Keywords
 Resolvent transform
 SU(1, 1)
 Spectral synthesis
 Spherical functions
 Two circles theorems
 Wiener’s theorem
 μharmonic functions
ASJC Scopus subject areas
 General Mathematics
 Applied Mathematics