Some Sharp L^2 Inequalities for Dirac Type Operators

Details Some Sharp L^2 Inequalities for Dirac Type Operators Some Sharp L^2 Inequalities for Dirac Type Operators

2007-11-25

arxiv.org/abs/0711.3905v1

SIGMA 3 (2007), 114, 10 pages

Physics

Mathematical Physics

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in

Scientific paper

10.3842/SIGMA.2007.114

We use the spectra of Dirac type operators on the sphere $S^{n}$ to produce
sharp $L^{2}$ inequalities on the sphere. These operators include the Dirac
operator on $S^{n}$, 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 $\mathbb{R}^{n}$.

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