【摘要】 本文得到了么模群Ｇ上酉表示的不可约性的一个等价刻画．即若ｆ是Ｇ上正定函数，π是Ｇ在Ｈｉｌｂｅｒｔ空间Ｈ上的酉表示，ｕ∈Ｈ是 Ｈ的拓扑生成元且ｆ（ｘ）＝（π（ｘ）ｕ，ｕ），则ｆ是不可分解的正定函数的充要条件是π是不可约酉表示．并将这一结果应用到ＳＵ（２），ＳＬ（２，Ｒ）上．更多还原

【Abstract】 An equivalent characterization of an irreducible unitary representation on unimodular group G is obtained, i.e., if f is a positive definite function on G, π is a unitary representation of G on a Hilbert space H, u ∈ H is a topological generator of H and f(x) = (π(x)u, u), then the positive definite function f on G is irreducible if and only if the unitary representation π is irreducible. Applications to SU(2), SL(2, R) are also given.更多还原