Constructive approximation of convergent sequences by eigenvalue sequences of radial Toeplitz–Fock operators

期刊论文
出版模式：

开放获取
发表日期：

2026年8月4日

查看全文

Kevin Esmeral García,
Egor A. Maximenko

摘要

It is well known that for every measurable function a, essentially bounded on the positive halfline, the corresponding radial Toeplitz operator $T_a$ $T_{a}$ , acting in the Segal–Bargmann–Fock space, is diagonal with respect to the canonical orthonormal basis consisting of normalized monomials. We denote by $\gamma _a$ $γ_{a}$ the corresponding eigenvalues sequence. Given an arbitrary convergent sequence, we uniformly approximate it by sequences of the form $\gamma _a$ $γ_{a}$ with any desired precision. We give a simple recipe for constructing a in terms of Laguerre polynomials. Previously, we proved this approximation result with non-constructive tools (Esmeral and Maximenko in Complex Anal. Oper. Theory 10, 2016). In the present paper, we also include some properties of the sequences $\gamma _a$ $γ_{a}$ and some properties of bounded sequences, uniformly continuous with respect to the sqrt-distance on natural numbers.