$L^2$ Serre Duality on Domains in Complex Manifolds and Applications

Abstract

An $L^2$ version of the Serre duality on domains in complex manifolds involving duality of Hilbert space realizations of the $\bar{\partial }$-operator is established. This duality is used to study the solution of the $\bar{\partial }$-equation with prescribed support. Applications are given to $\bar{\partial }$-closed extension of forms, as well to Bochner-Hartogs type extension of CR functions.

Typos corrected and new references added. To appear in the Transactions of the AMS

Cited by in corpus (1)

• L2 d-bar cohomology groups of some singular complex spaces