Spherical Representation for Solutions of the Convolution Equations on the Group of Möbius Transformations of the Unit Disk

Let G=PSL(2,R) be the group of Möbius transformations of the unit disk and T be a compactly supported distribution on G invariant under conjgations from the subgroup K=SO(2) . We study the problem of expansion of an arbitrary function f∈ C∞(G) satisfying the convolution equation f T=0 on the group G in a series in its elementary solutions. We solve both this problem and its local analog for a broad class of convolutors T .