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

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

2010-06-16

arxiv.org/abs/1006.3117v2

Mathematics

Complex Variables

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

Scientific paper

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.

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