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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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