线性时滞系统的Riesz基生成问题

On Riesz Basis of Linear Delay System

Riesz基问题是分布参数理论的基础问题之一.文章研究Hibert空间M2([hp,0];Cn)上时滞系统的广义本征元的Riesz基生成问题,给出了一个例子,使得其本征元不为其状态空间M2([-1,0];C2)上的Riesz基.

Problem of Riesz base is one of the fundamental problem of distributed perameter systems theory. We deal with Riesz bass of the generalied eigefunctions of a Delay system in the Hilbert space M2 （[hp,0];C^n）,we give an example that the eigenfunctions of a Linear Delay system do not form a Riesz basis for the state space M2（[-1,0];C^2）.