Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 114, 10 pages      arXiv:0711.3905      https://doi.org/10.3842/SIGMA.2007.114
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Some Sharp L2 Inequalities for Dirac Type Operators

Alexander Balinsky a and John Ryan b
a) Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF 24 4AG, UK
b) Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA

Received August 31, 2007, in final form November 14, 2007; Published online November 25, 2007

Abstract
We use the spectra of Dirac type operators on the sphere Sn to produce sharp L2 inequalities on the sphere. These operators include the Dirac operator on Sn, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in Rn.

Key words: Dirac operator; Clifford algebra; conformal Laplacian; Paenitz operator.

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