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

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics 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。

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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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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.