相关论文: Szego limit theorems

Szeg\H{o}'s First Limit Theorem provides the limiting statistical distribution (LSD) of the eigenvalues of large Toeplitz matrices. Szeg\H{o}'s Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order correction to the…

We discuss generalizations of the Szeg\H{o} Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems.…

In this paper, we consider the first Szeg\H{o} limit theorems on $d$-torus $\mathbb{T}^d$ for $1\leq d\leq +\infty$. It is shown that for any F{\o}lner sequence $\{\sigma_N\}$ of $\mathbb{Z}^d$ and $\varphi\in L^1_+(\mathbb{T}^d)$, it holds…

The Szeg\H{o} limit theorem by Fedele and Gebert for matrices of the type identity minus Hankel matrix is proved for the special case $1-\frac{\beta}{\pi}H_{N,\alpha}$ where $H_{N,\alpha}$ is the $N\times N$-Hilbert matrix,…

The Szego-Widom theorem provides an expression for the determinant of block Toeplitz matrices in the asymptotic limit of large matrix dimension n. We show that the presence of zero modes, i.e, eigenvalues that vanish as \alpha^n,…

We state and prove a version of Szeg\H{o}'s first limit theorem for Toeplitz-like operators on the Drury-Arveson space in the unit ball.

We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are $\mu$-distributed for some probability measure. As an application…

We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szeg\H{o}'s theorem. As a by-product, we also obtain an elementary proof of the…

We prove the following higher-order Szego theorems: if a measure on the unit circle has absolutely continuous part $w(\theta)$ and Verblunsky coefficients $\alpha$ with square-summable variation, then for any positive integer $m$, $\int…

This work provides the general framework for obtaining strong Szeg\H{o} limit theorems for multi-bordered, semi-framed, framed, and multi-framed Toeplitz determinants, extending the results of Basor et al. (2022) beyond the (single)…

In this paper, we extend some classical results of the Szego theory of orthogonal polynomials on the unit circle to the infinite-dimensional case, and we establish the corresponding Szego limit theorem.

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in…

We discuss an analogue of the First Szeg\H{o} Limit Theorem for multiplicative Toeplitz operators and highlight the role of the multliplicative F{\o}lner condition in this topic.

We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erd\"os-Moser problem). The main tools are Minkowski's theorem on…

We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…

In this paper, we prove a Szeg\"{o} type limit theorem on $\ell^2(\ZZ^d)$. We consider operators of the form $H=\Delta+V$, $V$ multiplication by a positive sequence $\{V(n), n \in \ZZ^d\}$ with $V(n) \rightarrow \infty, |n| \rightarrow…

We obtain a Szeg\"o limit theorem for a family of Toeplitz operators defined on the weighted Bergman space of the unit ball $\mathbb{B}_{n}$. The symbols of these operators are supported on some isotropic or co-isotropic submanifold $\Gamma…

We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket to formulate and prove analogues of the strong Szego limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of…

This is a detailed version of the paper math.FA/0212273. The main motivation for this work was to find an explicit formula for a "Szego-regularized" determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll manifold. The…

We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix…