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摘要严格奇异算子的概念是由 Kato在处理扰动理论时提出，其概念是研究积分算子，紧算子和无界算子的一个重要工具。并且 Kato指出，当X是 Hilbert空间，若算子 T∈B(X)，则在由算子 T 构成的算子空间中，严格奇异算子就是紧算子，而在二阶常微分算子谱理论的研究中，当λ为正则点，其预解式 R(λ，T)是以Green 函数为核的积分算子，且为紧算子。由此我们可以得出一些二阶常微分算子的性质。59687
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毕业论文关键词 严格奇异算子 紧算子 二阶常微分算子 谱理论 Green 函数
Title Strictly Singular Operators And Its Application
Abstract The concept of a strictly singular operator was introduced by Kato.T in his treatment of perturbation theory. It’s an important tool to deal with integration equation, compact operators and unbounded operators. And in Kato[11],page 288 has shown that the class of strictly singular operators and the class of precompact operators coincide in the space of bounded operators mapping a Hilbert space into a Hilbert space. In the survey of second-order ordinary differential operators, we can find that if λ is a resolvent point, then R(λ,T)is an integral operator of Green function, and itself is a compact operator.
Keywords strictly singular operator compact operator second-order ordinary operator spectrum theory Green function