The leading term of the spectral asymptotics for the Kohn-Laplace operator in a bounded domain

We prove the Weyl asymptotic formula for the number of eigenvalues of the Kohn-Laplace operator on a Heisenberg group and write out the leading term of asymptotics. The method of study is based on estimates of the Green function for the Dirichlet problem for the corresponding parabolic operator and makes use of the classical Hardy-Littlewood Tauberian theorem.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 493–505, October, 1998.This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00443 and No. 96-01-00503.