The paper under review deals with two different generalizations of the Heisenberg uncertainty principle. Let \((G,K)\) denote a Gelfand pair where \(G\) denotes a unimodular locally compact topological group and \(K\hookrightarrow G\) a compact subgroup [J. Dieudonné, Treatise on analysis, Volume VI (1978; Zbl 0435.43001); W. Schempp and B. Dreseler, Einführung in die harmonische Analyse (Stuttgart 1980; Zbl 0442.43001)]. The first generalization extends the uncertainty principle to functions on the double coset space \(K \setminus G/K\). It depends on the spherical transform for \((G,K)\) and the resulting decomposition of \(L^2 (K\setminus G/K) =L^2(G/K) \cap L^2(K \setminus G)\) by zonal spherical functions on \(G\) relative to \(K\) which are of positive type. The second generalization extends the uncertainty principles to the coset space \(G/K\). It depends on the vector valued transform corresponding to a direct integral decomposition of \(L^2(G/K)\). These two extensions are in reality equivalent to the fact that the underlying \(L^2\) decompositions are based on the same Plancherel measure. The Gelfand pair setting includes Riemannian symmetric manifolds, compact topological groups, and abelian locally compact topological groups.