Resolvent kernel for the Kohn Laplacian on Heisenberg groups

Abstract

We present a formula that relates the Kohn Laplacian on Heisenberg groups and the magnetic Laplacian. Then we obtain the resolvent kernel for the Kohn Laplacian and find its spectral density. We conclude by obtaining the Green kernel for fractional powers of the Kohn Laplacian.

Keywords

• Kohn Laplacian
• Heisenberg group
• magnetic Laplacian
• resolvent kernel
• Green kernel
• spectral density.