reinhardt域上szegÖ核的Forelli-rudin构造及渐近展开

Pub Date : 2015-10-01 DOI:10.18910/57651

M. Engliš, Hao Xu

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引用次数: 1

摘要

应用Forelli-Rudin构造和Nakazawa的hodograph变换，证明了严格伪凸完全Reinhardt域上szgo核渐近展开中不变理论系数的图论封闭公式。该公式提供了Bergman核和Szego核的渐近展开之间的结构类比。它可以有效地计算CR不变量中Fefferman渐近展开式的第一项。我们的方法也适用于Hirachi和Komatsu引入的Sobolev-Bergman核的渐近展开。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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FORELLI–RUDIN CONSTRUCTION AND ASYMPTOTIC EXPANSION OF SZEGÖ KERNEL ON REINHARDT DOMAINS

We apply Forelli-Rudin construction and Nakazawa’s hodograph transformation to prove a graph theoretic closed formula for invariant theoretic coefficients in the asymptotic expansion of the Szego kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szego kernels. It can be used to effectively compute the first terms of Fefferman’s asymptotic expansion in CR invariants. Our method also works for the asymptotic expansion of the Sobolev-Bergman kernel introduced by Hirachi and Komatsu.

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