广义C_0半群的谱映射定理

Spectral Mapping Theorem of Generalized C_0-Semigroup

传统的 C0 半群在诸如广义动态经济系统、电网系统及时滞微分方程等形如ddt(Cx(t) ) =Ax(t) +Bu(t) (其中 C不可逆 ) 中得不到直接应用 .为此引入广义 C0 半群来研究初值问题ddt(Cx(t) ) =Ax(t)Cx(0 ) =Cy.为了讨论其解的稳定性 (也即广义 C0 半群的稳定性 ) ,引入广义 C0 半群的 C生成元 A的 C谱 ,用 Banach代数中的谱理论方法得到了广义 C0

The traditional C 0 semigroup can not directly be used to study such as generalized dynamic economy system and electricity network system and retarded differential equation which formulate as dd t(Cx(t))=Ax(t)+Bu(t), where C is not reversible linear operator. To solve this problem, the generalized C 0 semigroup to study the following initial value problem dd t(Cx(t))=Ax(t) Cx(0)=Cy is introduced.Further in order to discuss the stability of the solution (that is the stability of generalized C 0 semigroup), C spectrum of the generator of generalized C 0 semigroup A is introduced. By the spectrum method of Banach algebra the spectrum mapping theorem of generalized C 0 semigroup is proved under this generalized spectrum.