相关论文: Characterisation of Ces\`aro and $L$-Asymptotic Li…

We investigate the extremal values of partial traces of matrix tensors under operator norm constraints. To evaluate these multi-linear quantities, we develop a comprehensive graphical formalism that encodes multi-leg partial traces, partial…

Asymptotic velocity is defined as the Ces\`aro limit of velocity. As such, its existence has been proven for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here we show for a class…

We study the properties of the Volterra and Ces\`aro operators viewed on the $L^1$-M\"untz space $M_\Lambda^1$ with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from…

The Ces\`aro limit - the asymptotic average of a sequence of real numbers - is an operator of fundamental importance in probability, statistics and analysis. Surprisingly, spaces of sequences with Ces\`aro limits have not previously been…

In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of potentials are considered. For bounded Hermitian potentials $V$…

In this paper, we introduce and investigate the notion of the Ces\'aro operator $C_{\mathscr T}$ on a rooted directed tree $\mathscr T.$ When $\mathscr T$ is the rooted tree with no branching vertex, then $C_{\mathscr T}$ is unitarily…

The notion of isometric and unitary asymptotes was introduced for power bounded operators in 1989 and was generalized in 2016--2019 by K\'erchy. In particular, it was shown that there exist operators without unitary asymptote. In this paper…

Let $\mu$ be a matrix-valued measure with the essential spectrum a single interval and countably many point masses outside of it. Under the assumption that the absolutely continuous part of $\mu$ satisfies Szego's condition and the point…

Any sequence of uniformly bounded $N\times N$ Hermitian Toeplitz matrices $\{\boldsymbol{H}_N\}$ is asymptotically equivalent to a certain sequence of $N\times N$ circulant matrices $\{\boldsymbol{C}_N\}$ derived from the Toeplitz matrices…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…

The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…

The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…

We study the asymptotic behaviour of orbits $(T^nx)_{n\ge0}$ of the classical Ces\`aro operator $T$ for sequences $x$ in the Banach space $c$ of convergent sequences. We give new non-probabilistic proofs, based on the Katznelson-Tzafriri…

A detailed investigation is made of the continuity, spectrum and mean ergodic properties of the Ces\`aro operator $C$ when acting on the strong duals of power series spaces of infinite type. There is a dramatic difference in the nature of…

Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…

This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the…

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,…

We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general matrix-valued Schr\"odinger operators on a half-line.

In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group…