Spectrum of the \(\overline\partial\)-Neumann Laplacian on the Fock space (Q1947335)

The author computes the spectrum of the \(\overline\partial\)-Neumann Laplacian on the Fock space \(L^2(\mathbb{C}^n,e^{-|z|^2})\) explicitly. It consists of positive integer eigenvalues each of which is of infinite multiplicity. It follows that the corresponding \(\overline\partial\)-Neumann operator fails to be with compact resolvent. As an application of the main result, the author obtains the same statement for the spectrum of the complex Witten Laplacian.