This manuscript deals with the explicit construction of the Green’s function of the Kohn Laplacian on a family of model domains. We are going to use two methods to handle this challenge. The first approach is to use spherical harmonics and special functions. The second approach is using the complex and real Hamiltonian and Lagrange formalism developed in the context of the sub-Riemannian manifolds. Here, we present not only the required details of the calculations of our main results, but also certain prerequisites and some additional materials which we hope will give the reader a clearer view of the entire subject.
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