On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group

TL;DR

This paper extends Kac's principle of not feeling the boundary to the Kohn Laplacian on the Heisenberg group, constructing integral boundary conditions and analyzing traces of Newton potentials, including higher powers.

Contribution

It introduces an integral boundary condition for the Kohn Laplacian on the Heisenberg group and characterizes the trace of associated Newton potentials, extending classical principles.

Findings

Constructed integral boundary conditions for the Kohn Laplacian.

Characterized the trace of Newton potentials on smooth surfaces.

Extended results to higher powers of the Kohn Laplacian.

Abstract

In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.