论文标题
汉克尔操作员的反向频谱问题的动态系统方法：一般情况
A Dynamical System Approach To The Inverse Spectral Problem For Hankel Operators: The General Case
论文作者
论文摘要
我们研究一般情况下汉克尔运营商的逆问题。在Gérard的工作之后，Grellier的工作是从Hankel运营商$γ$和$γs$的一对频谱数据中获得的，其中$ s $是Shift Operator。 复杂的对称操作员的理论为频谱数据的描述提供了便捷的语言。我们介绍了一般情况下的抽象光谱数据，并使用动力学系统方法将问题减少到由光谱数据构建的某些收缩的渐近稳定性。 渐近稳定性通常是问题的困难部分，但是在盖拉德（Gérard）之前的调查中，紧凑型操作员的案例几乎可以免费获得。 对于紧凑型运算符的情况，我们将抽象光谱数据的具体表示为两个相互键的序列，以及两个有限支持的概率度量的序列。这种表示与杰拉德（Gérard）治疗的一种不同，我们将翻译从一种语言到另一种语言提供。克拉克措施的理论在那里具有工具性。
We study the inverse problem for the Hankel operators in the general case. Following the work of Gérard--Grellier, the spectral data is obtained from the pair of Hankel operators $Γ$ and $ΓS$, where $S$ is the shift operator. The theory of complex symmetric operators provides a convenient language for the description of the spectral data. We introduce the abstract spectral data for the general case, and use the dynamical system approach, to reduce the problem to asymptotic stability of some contraction, constructed from the spectral data. The asymptotic stability is usually the hard part of the problem, but in the investigated earlier by Gérard--Grellier case of compact operators we get it almost for free. For the case of compact operators we get a concrete representation of the abstract spectral data as two intertwining sequences of singular values, and two sequences of finitely supported probability measures. This representation is different from one treated by Gérard--Grellier, and we provide the translation from one language to the other; theory of Clark measures is instrumental there.
