A Tauberian Approach to Weyl's Law for the Kohn Laplacian on Spheres

TL;DR

This paper derives the leading term in the eigenvalue distribution of the Kohn Laplacian on spheres using a Tauberian approach, providing explicit formulas as sums and integrals.

Contribution

It introduces a novel Tauberian method to compute the asymptotic eigenvalue count for the Kohn Laplacian on spheres, with explicit coefficient formulas.

Findings

Explicit asymptotic coefficient expressed as an infinite sum.

Integral representation of the leading coefficient.

Enhanced understanding of spectral asymptotics for the Kohn Laplacian.

Abstract

We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral.