𝐿² Serre duality on domains in complex manifolds and applications

Chakrabarti, Debraj; Shaw, Mei-Chi

doi:10.1090/S0002-9947-2012-05511-5

$L^2$ Serre duality on domains in complex manifolds and applications
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Trans. Amer. Math. Soc. 364 (2012), 3529-3554 Request permission

Abstract:

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

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