Compactness of the solution operator to ∂ in weighted L2-spaces ✩

In this paper we discuss compactness of the canonical solution operator to ∂ on weigthed L2 spaces on Cn. For this purpose we apply ideas which were used for the Witten Laplacian in the real case and various methods of spectral theory of these operators. We also point out connections to the theory of Dirac and Pauli operators. © 2006 Elsevier Inc. All rights reserved.