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- W1988353340 abstract "For a Dirac operator (D_{bar{g}}) over a spin compact Riemannian manifold with boundary ((bar{X},bar{g})), we give a new construction of the Calderon projector on (partialbar{X}) and of the associated Bergman projector on the space of L2 harmonic spinors on (bar{X}), and we analyze their Schwartz kernels. Our approach is based on the conformal covariance of (D_{bar{g}}) and the scattering theory for the Dirac operator associated with the complete conformal metric (g=bar{g}/rho^{2}) where ρ is a smooth function on (bar{X}) which equals the distance to the boundary near (partialbar{X}). We show that (frac{1}{2}(operatorname{Id}+tilde{S}(0))) is the orthogonal Calderon projector, where (tilde{S}(lambda)) is the holomorphic family in {ℜ(λ)≥0} of normalized scattering operators constructed in Guillarmou et al. (Adv. Math., 225(5):2464–2516, 2010), 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." @default.
- W1988353340 created "2016-06-24" @default.
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- W1988353340 date "2010-09-16" @default.
- W1988353340 modified "2023-10-16" @default.
- W1988353340 title "Bergman and Calderón projectors for Dirac operators" @default.
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