Spectral Synthesis in Fourier Algebras of Ultrapherical Hypergroups

Let H be an ultraspherical hypergroup associated to a locally compact group G and a spherical projector π (in Muruganandam, Math. Nachr. 281:1590–1603, 2008). We investigate spectral synthesis properties of the Fourier algebra A(H), partly building on results for A(G). Special emphasis is placed on double coset hypergroups. We also present several examples displaying the diverse behavior of hypergroups in contrast to groups.