等距半群的扰动
On the Perturbation of Isometric Groups
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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.Abstract: LetAbe the infinitesimal generator of an isometric group on a Hilbert spaceHandBbe the perturbed operator ofA. Assume thatBis dissymmetrical and its relative boundary aboutAis smaller than one. Using perturbation theorems ofm-dissipative operation and self-adjoint operators, itwas proved thatA +Bis also an infinitesimal generator of the isometric group. An example of Schr dinger equation with initial value problemwas presented to illustrate the obtained results.
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Key words:
- dissipation /
- perturbation /
- isometric semigroups /
- contractive semigroup
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