【摘要】 讨论了指数有界的n次积分C-半群的收敛性和算子列的逼近问题.证明了在同一空间上,不同n次积分C-半群的生成元可以交换.给出了误差估计的积分表示.由此得出:Banach空间Xk上n次积分C-半群序列Sk(t)强收敛于Banach空间X上n次积分C-半群S(t)的充分条件是其生成元序列Ak强收敛于A,并将这一结论推广到一般的Banach空间序列上.更多还原

【Abstract】 Convergence for exponentially bounded n-times integrated C-semigroups and approximation problem for a sequence of operators were discussed.The interchangeability of generators on the same space for different n-times integrated C-semigroups was proved.The integral representation of error estimate was obtained,which results in the main theorem as follows: an exponentially bounded n-times integrated C-semigroup S(t) on a Banach space X was approximated by a sequence of exponentially bounded n-times integrated C-semigroups S_k(t) on spaces X_k if and only if A_k converges to A.The result is generalized to a sequence of Banach spaces.更多还原