本文在可分的Ｂａｎａｃｈ空间研究Ｒｉｅｓｚ半群无穷小母元广义本征函数系统的完整性，利用母元的予解式和谱分布，我们给出予解式的级为有限时广义本征函数系统完整性的判定．

In this paper we study the completeness of system of generalized eigenfunctions of A, which is the infinitesimal generator of a Riesz semigroup in a separable Banach space. In view of the resolvent and the spectral distribution of A, we present the criterion of completeness of system of generalized eigenfunction of A with resolvent of order p < +∞.