Analytic Singularities of the Bergman Kernel for Tubes
نویسنده
چکیده
Let ⊂ R be a bounded, convex, and open set with real analytic boundary. Let T ⊂ C be the tube with base , and let B be the Bergman kernel of T . If is strongly convex, then B is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation we relate the off-diagonal points where analyticity fails to the characteristic lines. These lines are contained in the boundary of T , and they are projections of the Treves curves. These curves are symplectic invariants that are determined by the CR (Cauchy-Riemann) structure of the boundary of T . Note that Treves curves exist only when has at least one weakly convex boundary point.
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