Proceedings of the American Mathematical Society

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

Author(s): Roberto Camporesi; Emmanuel Pedon
Journal: Proc. Amer. Math. Soc. 130 (2002), 507-516.
MSC (2000): Primary 43A85, 58J50; Secondary 34L40, 53C27, 53C35
Posted: July 25, 2001
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The continuous spectrum of the Dirac operator

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

even, where $\mathop{\rm spec}\nolimits_c(D)=(-\infty,-\frac{1}{2}]\cup [\frac{1}{2},+\infty)$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A85, 58J50, 34L40, 53C27, 53C35

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: 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
Posted: July 25, 2001
Additional Notes: The second author was supported by the European Commission (TMR 1998-2001 Network {\it Harmonic Analysis})
Communicated by: Rebecca Herb
Copyright of article: Copyright 2001, American Mathematical Society

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