L² Serre Duality on Domains in Complex Manifolds and Applications

2010/06/16 by Chakrabarti, Debraj, Shaw, Mei-Chi · 1 citation
#32C37 #32W05 #35N15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.3117

Abstract

An L² 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 to Bochner-Hartogs type extension of CR functions.

Cited by

• L²-Sobolev Theory for ∂ on Domains in \Bbb CPⁿ

Related

• L²-Serre duality on singular complex spaces and applications
• L²-Serre duality on singular complex spaces and rational singularities
• The ∂-equation, duality, and holomorphic forms on a reduced complex space
• Serre duality and Hörmander's solution of the ∂ -equation
• Solving the ∂ ∂ with prescribed support