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15 June 2001 Analytic singularities of the Bergman kernel for tubes
Gábor Francsics, Nicholas Hanges
Duke Math. J. 108(3): 539-580 (15 June 2001). DOI: 10.1215/S0012-7094-01-10835-1

Abstract

Let Ω⊂ℝn be a bounded, convex, and open set with real analytic boundary. Let TΩ⊂ℂn be the tube with base Ω, and let $\mathcal{B}$ be the Bergman kernel of TΩ. If Ω is strongly convex, then $\mathcal{B}$ 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 TΩ, 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 TΩ. Note that Treves curves exist only when Ω has at least one weakly convex boundary point.

Citation

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Gábor Francsics. Nicholas Hanges. "Analytic singularities of the Bergman kernel for tubes." Duke Math. J. 108 (3) 539 - 580, 15 June 2001. https://doi.org/10.1215/S0012-7094-01-10835-1

Information

Published: 15 June 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1016.32014
MathSciNet: MR1838661
Digital Object Identifier: 10.1215/S0012-7094-01-10835-1

Subjects:
Primary: 32T27
Secondary: 32A25 , 35H10

Rights: Copyright © 2001 Duke University Press

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Vol.108 • No. 3 • 15 June 2001
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