Szegö limit theorem and Heisenberg Laplacian

Abstract

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