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$ L^2$ Serre duality on domains in complex manifolds and applications


Authors: Debraj Chakrabarti and Mei-Chi Shaw
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
Published electronically: March 6, 2012
MathSciNet review: 2901223
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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.


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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
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
Email: mei-chi.shaw.1@nd.edu

DOI: https://doi.org/10.1090/S0002-9947-2012-05511-5
Keywords: Serre duality, Cauchy-Riemann equation
Received by editor(s): June 15, 2010
Published electronically: March 6, 2012
Additional Notes: The second-named author was partially supported by NSF grants.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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