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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

The Dirichlet to Neumann operator for elliptic complexes


Author: N. Tarkhanov
Journal: Trans. Amer. Math. Soc. 363 (2011), 6421-6437
MSC (2010): Primary 58J10; Secondary 35R30
Published electronically: July 22, 2011
MathSciNet review: 2833561
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Abstract: We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.


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Additional Information

N. Tarkhanov
Affiliation: Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany
Email: tarkhanov@math.uni-potsdam.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05460-7
Keywords: Elliptic complexes, Dirichlet to Neumann operator, inverse problems
Received by editor(s): November 23, 2009
Published electronically: July 22, 2011
Article copyright: © Copyright 2011 American Mathematical Society



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