等距半群的扰动  

On the Perturbation of Isometric Groups

作　　者：谢灵红[1] 谢建华[2] 

机构地区：[1]西南交通大学应用数学系,四川成都610031 [2]西南交通大学应用力学与工程系,四川成都610031

出　　处：《西南交通大学学报》2004年第4期547-549,共3页Journal of Southwest Jiaotong University

摘　　要：对于Hilbert空间H上等距群的无穷小生成元A,在其扰动算子B是反对称算子且关于A的相对界小于1的条件下,利用m 保守耗散算子和自伴算子的扰动定理,证明扰动后算子A+B仍然是等距群的无穷小生成元,并以Schr dinger方程的初值问题为例说明了所得结果.Let A be the infinitesimal generator of an isometric group on a Hilbert space H and B be the perturbed operator of A. Assume that B is dissymmetrical and its relative boundary about A is smaller than one. Using perturbation theorems of m-dissipative operation and self-adjoint operators, it was proved that A+B is also an infinitesimal generator of the isometric group. An example of Schrdinger equation with initial value problem was presented to illustrate the obtained results.

关 键 词：耗散 扰动 等距半群 收缩半群 HILBERT空间 扰动算子 扰动定理 无穷小生成元 

分 类 号：O152.7[理学—数学]