L 2 Serre duality on domains in complex manifolds and applications

Debraj Chakrabarti, Mei Chi Shaw

Research output: Contribution to journalArticlepeer-review

22 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 languageEnglish
Pages (from-to)3529-3554
Number of pages26
JournalTransactions of the American Mathematical Society
Volume364
Issue number7
DOIs
StatePublished - Mar 6 2012

Keywords

  • Cauchy-Riemann equation
  • Serre duality

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