{"paper":{"title":"Bergman and Calder\\'on projectors for Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Colin Guillarmou, Jinsung Park, Sergiu Moroianu","submitted_at":"2010-09-16T13:58:24Z","abstract_excerpt":"For a Dirac operator $D_{\\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\\bar{X},\\bar{g})$, we give a natural construction of the Calder\\'on projector and of the associated Bergman projector on the space of 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 to the complete conformal metric $g=\\bar{g}/\\rho^2$ where $\\rho$ is a smooth function on $\\bar{X}$ which equals the distance to the boundary near $\\partial\\bar{X}$. We show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3179","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}