A Weyl Matrix Perspective on Unbounded Non-Self-Adjoint Jacobi Matrices.

IF 0.8 4区 数学 Q2 MATHEMATICS
Complex Analysis and Operator Theory Pub Date : 2025-01-01 Epub Date: 2025-09-23 DOI:10.1007/s11785-025-01804-5
Benjamin Eichinger, Milivoje Lukić, Giorgio Young
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引用次数: 0

Abstract

A new way of encoding a non-self-adjoint Jacobi matrix J by a spectral measure of |J| together with a phase function was described by Pushnitski-Štampach in the bounded case. We present another perspective on this correspondence, based on Weyl functions instead of moments, which simplifies some proofs and generalizes the correspondence to the unbounded case. In particular, we find a bijection between proper Jacobi matrices with positive off-diagonal elements, and a class of spectral data. We prove that this mapping is continuous in a suitable sense. To prove injectivity of the map, we prove a local Borg-Marchenko theorem for unbounded non-self-adjoint Jacobi matrices in this class that may be of independent interest.

无界非自伴随Jacobi矩阵的Weyl矩阵透视。
在有界情况下,Pushnitski-Štampach描述了用|J|的谱测度和相函数编码非自伴随Jacobi矩阵J的一种新方法。我们提出了另一种观点,基于Weyl函数而不是矩,简化了一些证明,并将这种对应推广到无界情况。特别地,我们找到了具有正非对角元素的雅可比矩阵与一类谱数据之间的双射。我们证明了这个映射在适当的意义上是连续的。为了证明映射的内射性,我们证明了一类具有独立意义的无界非自伴Jacobi矩阵的一个局部Borg-Marchenko定理。
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来源期刊
CiteScore
1.20
自引率
12.50%
发文量
107
审稿时长
3 months
期刊介绍: Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.
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