Szeg\"o limit theorem and Heisenberg Laplacian

Jiyu Fan; Ari Laptev

Szeg\"o limit theorem and Heisenberg Laplacian

Spectral Theory 2026-07-24 v1 Analysis of PDEs Functional Analysis

Authors: Jiyu Fan , Ari Laptev

Abstract

The aim of this paper is to obtain a version of the classical Szeg\"o limit theorem, where instead of the operator of second derivative on a circle we consider the Heisenberg-H\"ormander Laplacian in $L^2(\Bbb R^3)$ . Besides, we derive a sharp inequality for convex functions that we call Szeg\"o-type inequality.

Keywords

Szego limit theorem Heisenberg Laplacian Hormander Laplacian convex functions Szego-type inequality spectral asymptotics

Cite

@article{arxiv.2607.22431,
  title  = {Szeg\"o limit theorem and Heisenberg Laplacian},
  author = {Jiyu Fan and Ari Laptev},
  journal= {arXiv preprint arXiv:2607.22431},
  year   = {2026}
}