自伴Toeplitz算子的谱分析

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2019-06-17 DOI:10.7900/jot.2019jun19.2244

A. Sobolev, D. Yafaev

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引用次数: 2

摘要

本文追求三个目标。首先，我们提供了自伴Toeplitz算子的谱分析的扩展版本，该算子最初由M.Rosenblum在20世纪60年代建立。我们对Rosenblum的方法进行了一些改进：例如，我们对绝对连续性的证明，依赖于极限吸收原理的弱版本，更直接。其次，我们详细研究了具有有限谱多重性的Toeplitz算子。特别地，我们引入了广义本征函数，并研究了它们的性质。第三，我们对分段连续符号进行了更详细的谱分析。这对于构造具有这些符号的Toeplitz算子的散射理论是必要的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On spectral analysis of self-adjoint Toeplitz operators

The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for instance, our proof of the absolute continuity, relying on a weak version of the limiting absorption principle, is more direct. Secondly, we study in detail Toeplitz operators with finite spectral multiplicity. In particular, we introduce generalized eigenfunctions and investigate their properties. Thirdly, we develop a more detailed spectral analysis for piecewise continuous symbols. This is necessary for construction of scattering theory for Toeplitz operators with such symbols.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.