Here formula_77 denotes the formal adjoint of formula_72 with respect to formula_79 where the volume form may be derived from a contact form which is associated to the CR structure. See for example the paper of J.M. Lee in the American J. referred below. Note the Kohn Laplacian takes (0,p) forms to (0,p) forms. Functions that are annihilated by the Kohn Laplacian are called CR functions. They are the boundary analogs of holomorphic functions. The real parts of the CR functions are called the CR pluriharmonic functions. The Kohn Laplacian formula_80 is a non-negative, formally self-adjoint operator. It is degenerate and has a characteristic set where its symbol vanishes. On a compact, strongly pseudo-convex abstract CR manifold, it has discrete positive eigenvalues which go to infinity and also approach zero. The kernel consists of the CR functions and so is infinite dimensional. If the positive eigenvalues of the Kohn Laplacian are bounded below by a positive constant, then the Kohn Laplacian has closed range and conversely. Thus for embedded CR structures using the result of Kohn stated above, we conclude that the compact CR structure that is strongly pseudoconvex is embedded if and only if the Kohn Laplacian has positive eigenvalues that are bounded below by a positive constant. The Kohn Laplacian always has the eigenvalue zero corresponding to the CR functions.