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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The continuous spectrum of the Dirac operator on noncompact Riemannian symmetric spaces of rank one


Authors: Roberto Camporesi and Emmanuel Pedon
Journal: Proc. Amer. Math. Soc. 130 (2002), 507-516
MSC (2000): Primary 43A85, 58J50; Secondary 34L40, 53C27, 53C35
Published electronically: July 25, 2001
MathSciNet review: 1862131
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Abstract:

The continuous spectrum of the Dirac operator $D$ on the complex, quaternionic, and octonionic hyperbolic spaces is calculated using representation theory. It is proved that $\mathop{\rm spec}\nolimits_c(D)=\mathbb R$, except for the complex hyperbolic spaces $H^n(\mathbb C)$ with $n$ even, where $\mathop{\rm spec}\nolimits_c(D)=(-\infty,-\frac{1}{2}]\cup [\frac{1}{2},+\infty)$.


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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

Emmanuel Pedon
Affiliation: Laboratoire de Mathématiques, Université de Reims, UPRESA 6056, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 2, France
Email: emmanuel.pedon@univ-reims.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06294-3
PII: S 0002-9939(01)06294-3
Keywords: Hyperbolic spaces, spinors, Dirac operator, spectral theory
Received by editor(s): July 5, 2000
Published electronically: July 25, 2001
Additional Notes: The second author was supported by the European Commission (TMR 1998-2001 Network Harmonic Analysis)
Communicated by: Rebecca Herb
Article copyright: © Copyright 2001 American Mathematical Society