Essential self-adjointness, generalized eigenforms, and spectra for the \(\bar {\partial}\)-Neumann problem on G-manifolds (Q647593)

The authors investigate complex manifolds with boundary which are also the total space of a principal \(G\)-bundle. Here \(G\) is a Lie group and the orbit space is assumed to be compact. Then it is shown that the \(\overline{\partial}\)-Neumann Laplacian is essentially self-adjoint on its restriction to compactly supported smooth forms. The relation between the spectrum and the existence of generalized eigenforms is investigated.