C＿0半群解析延拓问题的一个注记

A Note on Analytic Extension of C_0-semigroups

关于解析半群，一个重要结论说明，对给定的一致有界Ｃ＿０半群来说，它在某个扇形区域△＿δ内的可解析延拓性与该半群的无穷小生成元在某个复数集∑＿η上的性质有密切关系￣［１］，然而参数δ与η之间的关系至今尚没弄清楚。本文所给的结果使得半群的一个重要的解析性结论更加完善，彻底搞清了δ与η之间的关系，并把所得结果推广到了一般Ｃ＿０半群和区域△＿δ关于实轴不对称的情形。

In analytic semigroup theory,an important result shows that the analyticextensibility to an infinite sector△_δ of an uniformly bounded C_0-semigroup is closely re-lated to the spectral property of its infinitesimal generator in a set∑_ηof complex numbers.However,the relation between δ and η is still not clear.In this paper an important result onanalytic semigroup￣[1] is improved,the exact relation between δ and ηis given,and Our re-sult is generalized to the case when the semigroup considered is general C_0-semigroup andthe sector △_δis not symmetric with respect to the real axis。