Related papers: A Szeg\H{o} limit theorem for translation-invarian…

We prove full Szeg\H{o}-type large-box trace asymptotics for selfadjoint $\mathbb{Z}^d$-ergodic operators $\Omega\ni \omega\mapsto H_\omega$ acting on $L^2(\mathbb{R}^d)$. More precisely, let $g$ be a bounded, compactly supported and…

We consider a regularised Fermi projection of the Hamiltonian of the massless Dirac equation at Fermi energy zero. The matrix-valued symbol of the resulting operator is discontinuous in the origin. For this operator, we prove Szeg\H{o}-type…

We continue studying polynomials generated by the Szeg\H{o} recursion when a finite number of Verblunsky coefficients lie outside the closed unit disk. We prove some asymptotic results for the corresponding orthogonal polynomials and then…

This article concerns the asymptotics of pseudodifferential operators whose Weyl symbol is the convolution of a discontinuous function dilated by a large scaling parameter with a smooth function of constant scale. These operators include as…

We consider a multi-dimensional continuum Schr\"odinger operator $H$ which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the…

The main result in this paper is a one term Szego type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are allowed to be non-smooth or discontinuous in…

The paper is a continuation of work [15] in which the general setting for analogs of the Szeg\"o theorem for ergodic operators was given and several interesting cases were considered. Here we extend the results of [15] to a wider class of…

The classical Szeg\"o 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…

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…

We continue to investigate some classes of Szeg\"o type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szeg\"o to this setting.

We study Schr\"odinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in $\lambda^{-\delta}$ with $\delta\in(0,1)$ for most of the…

In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…

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…

Let $S_g$ be a closed orientable surface of genus $g > 1$. Consider the minimal asymptotic translation length $L_{\mathcal{T}}(k, g)$ on the Teichm\"uller space of $S_g$, among pseudo-Anosov mapping classes of $S_g$ acting trivially on a…

We provide a representation in terms of certain canonical functions for a sequence of polynomials orthogonal with respect to a weight that is strictly positive and analytic on the unit circle. These formulas yield a complete asymptotic…

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 Szeg\"o…

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal…

We compute the leading and sub-leading terms in the asymptotic expansion of the Szeg\"o kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by…

We consider functions of multi-dimensional versions of truncated Wiener--Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the…

We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic $\alpha$-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the…