Functional Model of a Closed Non-Selfadjoint Operator
Functional Model of a Closed Non-Selfadjoint Operator
复制标题
闭非自伴算子的函数模型
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
V. Ryzhov
中科院分区：
文献类型：
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作者：
V. Ryzhov
摘要。构造了作用于可分离Hilbert空间上具有非空解集的任意闭算子的对称泛函模型。该结构基于Sz的显式形式。闭耗散算子的- nagy - foiaia模型，特征函数的Potapov-Ginzburg变换，以及某些可解恒等式。所有的考虑都是在最小的假设下进行的，得到的结果直接适用于数学物理中典型出现的问题。给出了参与模型构建的所有对象的显式公式。
Abstract.We construct the symmetric functional model of an arbitrary closed operator with non-empty resolvent set acting on a separable Hilbert space. The construction is based on the explicit form of the Sz.-Nagy-Foiaş model of a closed dissipative operator, the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried out under minimal assumptions, and obtained results are directly applicable to problems typically arising in mathematical physics. Explicit formulae for all the objects participating in the model construction are provided.