Harmonic analysis and spectral synthesis in central hypergroups (Q1092355)

A locally compact hypergroup K is called central if K/Z is compact where Z is the intersection of the maximal subgroup and the center of K. The dual space of K is shown to be a locally compact Hausdorff space. A Plancherel measure is defined that leads to a simple formulation of the Plancherel theorem and the inversion formula. \(L^ 1(K)\) is shown to be completely regular. It is shown that finite subsets of the dual space are spectral and that their \(L^ 1\)-kernels contain bounded approximate units.