Spectral estimates and asymptotics for stratified Lie groups

TL;DR

This paper develops spectral estimates and asymptotic formulas for operators on stratified Lie groups, enhancing understanding of their spectral properties and extending classical results to a broader geometric context.

Contribution

It introduces new spectral asymptotic formulas for operators related to sub-Laplacians on stratified Lie groups, using Cwikel-type estimates for singular values.

Findings

Derived novel spectral asymptotics for sub-Laplacian related operators

Established Cwikel-type estimates for singular values on stratified Lie groups

Extended classical spectral results to a non-commutative geometric setting

Abstract

We study Cwikel-type estimates for the singular values and Schatten $\mathcal{L}_p$-norms of compositions of multiplication and convolution operators acting on stratified Lie groups. This enables us to obtain novel spectral asymptotic formulas for certain operators derived from sub-Laplacians.