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BERGMAN AND CALDERÓN PROJECTORS FOR DIRAC OPERATORS

By Colin Guillarmou, Sergiu Moroianu and Jinsung Park

Abstract

Abstract. For a Dirac operator D¯g over a spin compact Riemannian manifold with boundary (X, g), we give a natural construction of the Calderón projector and of the associated Bergman projector on the space of harmonic spinors on X, and we analyze their Schwartz kernels. Our approach is based on the conformal covariance of D¯g and the analysis of the complete conformal metric g = g/ρ 2 where ρ is a smooth function on X which is equal to the distance to the boundary near ∂X. We then show that 1 2 (Id + e S(0)) is the orthogonal Calderón projector, where e S(λ) is the holomorphic family in {ℜ(λ) ≥ 0} of normalized scattering operators constructed in [24], which are classical pseudo-differential of order 2λ. Finally we construct natural conformally covariant odd powers of the Dirac operator on any compact spin manifold. 1

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.188.2915
Provided by: CiteSeerX
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