$L^2$ Serre duality on domains in complex manifolds and applications
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- by Debraj Chakrabarti and Mei-Chi Shaw PDF
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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 $\overline {\partial }$-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.References
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Additional Information
- Debraj Chakrabarti
- Affiliation: Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai –400 076, India
- Address at time of publication: TIFR Center for Applicable Mathematics, Sharada Nagar, Chikkabommasandra, Bangaluru 560065, India
- MR Author ID: 827655
- Email: dchakrab@iitb.ac.in, debraj@math.tifrbng.res.in
- Mei-Chi Shaw
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 160050
- Email: mei-chi.shaw.1@nd.edu
- Received by editor(s): June 15, 2010
- Published electronically: March 6, 2012
- Additional Notes: The second-named author was partially supported by NSF grants.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 3529-3554
- MSC (2010): Primary 32C37, 35N15, 32W05
- DOI: https://doi.org/10.1090/S0002-9947-2012-05511-5
- MathSciNet review: 2901223