Nikolai Nikolski, Alexander Pushnitski
We discuss an analogue of the First Szegő Limit Theorem for multiplicative Toeplitz operators and highlight the role of the multliplicative Følner condition in this topic.
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Szegő Limit Theorem for Truncated Toeplitz Operators
本文研究 Szegő 极限定理对截断 Toeplitz 算子的推广，提出有限维模型空间压缩情形下的新定理，并刻画了 Strouse-Timotin-Zarrabi 2017 年变体成立的序列条件。
We consider the determinants of compressions of Toeplitz operators to finite-dimensional model spaces and establish analogues of the Borodin-Okounkov formula and the strong Szegö limit theorem in this setting.
Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szegö type theorems concerning the asymptotics of their compressions to an increasing chain of finite dimensional model spaces.
A Semi-Classical Szegő-type Limit Theorem for Toeplitz Operators
本文研究了Toeplitz算子在加权Bergman空间和L²(G)上的Szego型极限定理，针对紧局部紧阿贝尔群分别给出形式化表达，并统一扩展了多个经典结果。
A Szegő Limit Theorem for Radially-Compressed Toeplitz Operators
该研究在复平面圆盘的再生核希尔伯特空间中建立Szegő型极限定理，推导Toeplitz算子压缩形式的特征值密度公式，并提供Bergman等空间实例，推进算子谱理论研究。
We formulate and establish a noncommutative version of the well known Helson-Szego theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to use this theorem to characterise the symbols of invertible Toeplitz operators on the noncommutative Hardy spaces associated to subdiagonal subalgebras.
A Szegö limit theorem for a class of Toeplitz operators on the Bergman space of the unit ball with singular symbols
本文针对单位球加权 Bergman 空间上符号支撑于迷向或余迷向子流形且关于 Lebesgue 测度奇异的一类 Toeplitz 算子，建立了 Szegö 极限定理，刻画了参数趋于无穷时的渐近行为。
At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szegö's strong limit theorem. The intention of this paper is to show that Jacobi's theorem on the minors of the inverse matrix remains one of the most comfortable tools for tackling the matter. We repeat a known proof of the Borodin-Okounkov formula and thus of the strong Szegö limit theorem that is based on Jacobi's theorem. We then use Jacobi's theorem to derive exact and asymptotic formulas for Toeplitz determinants generated by functions with nonzero winding number. This derivation is ne…
Szegő-Type Limit Theorem in the Drury-Arveson space
本研究针对单位球内Drury-Arveson空间上的类Toeplitz算子，提出并证明了Szegő第一极限定理的一个版本，拓展了该定理的适用空间范围。
The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections $P_n T(a) P_n$ of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.
In this paper the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUC's). There are four main results: the first concerns the approximation of the inverse of a Toeplitz operator by the inverses of its finite truncations. The second concerns a new proof of the `hard' part of Baxter's theorem, and the third concerns the Born approximation for a scattering problem on the lattice $\mathbb{Z}_+$. The fourth and final result concerns a basic proposition of Golinskii-Ib…
We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szegő limit theorem for symplectic eigenvalues, derive an expression for the entropy rate of stationary quantum Gaussian processes, and study the distribution of symplectic eigenvalues of truncated block Toeplitz matrices. We also introduce a concept of symplectic numerical range, analogous to that of numerical range, and study some of its basic properties, mainly in the context of block Toeplitz operators.
We establish versions of Szegő's distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear constraints. Each such algebra is naturally represented on a family of reproducing kernel Hilbert spaces, which play a central role in the proofs.
Bernstein-Markov measures and Toeplitz theory
本文证明在赋予大线丛的紧复流形上，与Bernstein-Markov测度关联的Toeplitz算子在复合下构成代数，并基于Bergman核非对角渐近分析推导出Szegő型谱等分布结果。
Toeplitz Operators on Contact Manifolds and Equivariant K-homology
本文通过等变K-同调理论推广了Boutet de Monvel的Toeplitz算子索引定理，证明Dirac算子与Szego投影在等变K-同调中确定相同类。
Given a CR manifold with non-degenerate Levi form, we show that the operators of the functional calculus for Toeplitz operators are complex Fourier integral operators of Szegő type. As an application, we establish semi-classical spectral dimensions for Toeplitz operators. We then consider a CR manifold with a compact Lie group action $G$ and we establish quantization commutes with reduction for Toeplitz operators. Moreover, we also compute semi-classical spectral dimensions for $G$-invariant Toeplitz operators.
Limiting eigenvalue distribution and entropy of multi-Toeplitz matrices
本文证明了d≥2时全Fock空间上多Toeplitz算子的Szegő第一极限定理，给出截断多Toeplitz算子特征值的极限分布及熵，其与经典d=1情形差异显著，纯原子测度可关联渗流过程。
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of the form $ (a_{i-j} \pm a_{i+j+1-k})_{i,j=0... N-1} $ with $k$ is fixed. We will show that this example as well as some general classes of operators have expansions that are similar to those that appear in the Strong Szegö Limit Theorem. We also obtain exact identitities for some of the determinants that are analogous to the one derived independently by Ger…
We consider the class of positive bounded and semi-continuous functions defined on the two dimensional torus If f belongs to this class, then f will be considered as the symbol of a Toeplitz operator truncated on a triangle parametrised by an integer number . We develop a geometric structure of the inverse of the Toeplitz operator and give an asymptotical development of the trace of its inverse wich brings out the geometry of the triangle. The foundation of this result consists in the possibility of f having a factorisation of type |g|^2 where the spectrum of g will be localised in a given sem…
A Representation Theoretic Approach to Toeplitz Quantization on Flag Manifolds
本文从表示论视角研究紧李群广义旗流形上的Toeplitz算子，证明其基本性质、识别大型交换族并实现Berezin变换为近似单位卷积，进而利用相关结果证明Szegö极限定理。
Free versions of the strong Szegő limit theorem
研究强塞格极限定理的多元推广，用独立随机酉矩阵系统代替单个酉矩阵，经典证明不适用，引入新工具，还得到酉矩阵束平均行列式及自由哈尔酉矩阵矩阵和谱半径公式等结果。
A Noncommutative Szegő-Type Theorem on the Row-Ball
本文借助非交换测度与 Schur 参数理论，建立 nc 测度和多 Toeplitz 核的对应，证明行球上的非交换 Szegő 型定理及正交多项式零点定理。
The first Szegő limit theorem on multi-dimensional torus
本文证明了多维环面上第一 Szegő 极限定理，包括有限维和无限维情形，并解决了 Nikolski 和 Pushnitski 提出的两个问题。
Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of op…
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