L 2 Serre duality on domains in complex manifolds and applications

Debraj Chakrabarti; Mei Chi Shaw

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

L ² Serre duality on domains in complex manifolds and applications

Debraj Chakrabarti, Mei Chi Shaw

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	3529-3554
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	364
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-2012-05511-5
State	Published - Mar 6 2012

Keywords

Cauchy-Riemann equation
Serre duality

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10.1090/S0002-9947-2012-05511-5

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abstract = "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.",

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AB - 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.

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L ² Serre duality on domains in complex manifolds and applications

Abstract

Keywords

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