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