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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 complex crown for homogeneous harmonic spaces


Authors: Roberto Camporesi and Bernhard Krötz
Journal: Trans. Amer. Math. Soc. 364 (2012), 2227-2240
MSC (2010): Primary 22E25, 22E46, 43A85
Published electronically: December 1, 2011
MathSciNet review: 2869205
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Abstract: The complex crown of a noncompact Riemannian symmetric space $ X=G/K$ is generalized to the case of homogeneous harmonic spaces $ S=NA$. We prove that every eigenfunction of the Laplace-Beltrami operator on $ S$ extends holomorphically to the crown, and that the crown is the maximal $ S$-invariant domain in $ S_{\mathbb{C}}$ with this property.


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Additional Information

Roberto Camporesi
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: camporesi@polito.it

Bernhard Krötz
Affiliation: Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
Email: kroetz@math.uni-hannover.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05571-6
PII: S 0002-9947(2011)05571-6
Keywords: Homogeneous harmonic spaces, complex crown
Received by editor(s): April 22, 2010
Received by editor(s) in revised form: August 17, 2010, December 14, 2010, February 1, 2011, and February 15, 2011
Published electronically: December 1, 2011
Article copyright: © Copyright 2011 American Mathematical Society