【摘要】 将Frechet空间X上的算子A的广义解空间拓扑化 ,证明了A在Zk+1上的限制生成k 次积分半群 ,并且在某种意义下 ,Zk +1是最大的 .应用上述结果 ,证明了A生成k 次积分半群的充要条件是对 x∈X ,积分Cauchy问题有唯一解 .更多还原

【Abstract】 We topologize Z k,the generalized solution space of the k-times integrated Cauchy Problem (ACP k) for closed operator A on a Frechet space X.We show that the restriction of A on Z k+1 generates a k-times integrated semigroup and Z k+1 is maximal in some sense. For its applications we show that A generates a k-times integrated semigroup if and only if there exists a unique solution of ACP k+1 for all x∈X.更多还原