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

Debraj Chakrabarti; Mei-Chi Shaw

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

Complex Variables 2010-12-06 v2

Authors: Debraj Chakrabarti , Mei-Chi Shaw

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.

Keywords

extension theorems pseudoconvex domains

Cite

@article{arxiv.1006.3117,
  title  = {$L^2$ Serre Duality on Domains in Complex Manifolds and Applications},
  author = {Debraj Chakrabarti and Mei-Chi Shaw},
  journal= {arXiv preprint arXiv:1006.3117},
  year   = {2010}
}

Comments

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

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