Spectrum is rational in dimension one

A Toeplitz-like operator with rational symbol having poles on the unit circle II: the spectrum

This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in ${\mathbb C}$. Various examples illustrate the results.

有限哈达玛对的有理谱及实直线上的有界谱集

Rational Spectra for Finite Hadamard Pairs and Bounded Spectral Sets on the real line

研究有限谱对\((A,\Gamma)\)等的有理谱问题，核心方法是利用广义范德蒙德系统的模刚性定理等，主要贡献是证明相关谱为有理谱，完善等价关系，简化一维富格莱德猜想。

具有单位圆上极点的有理矩阵符号的类Toeplitz算子：矩阵表示与谱分析

A Toeplitz-like operator with rational matrix symbol having poles on the unit circle:\ Matrix representation and spectral analysis

本文利用状态空间实现技术研究符号在单位圆上有极点的无界Toeplitz算子，建立其与半无限Toeplitz矩阵的联系，并确定本质谱与预解集。

Dimension-free $L^p$ estimates for vectors of Riesz transforms in the rational Dunkl setting

In this article, we prove dimension-free upper bound for the $L^p$-norms of the vector of Riesz transforms in the rational Dunkl setting. Our main technique is Bellman function method adapted to the Dunkl setting.

自由（半）圆算子中多项式的谱

The spectra of polynomials in free (semi)circular operators

研究自由半圆随机变量中有界有理函数的谱，证明其与L²谱一致，并计算自由圆随机变量多项式谱。

The failure of rational dilation on a triply connected domain

For R a bounded triply connected domain with boundary consisting of disjoint Jordan loops there exists an operator T on a complex Hilbert space H so that the closure of R is a spectral set for T, but T does not dilate to a normal operator with spectrum in B, the boundary of R. There is considerable overlap with the construction of an example on such a domain recently obtained by Agler, Harland and Rafael using numerical computations and work of Agler and Harland.