Osaka Journal of Mathematics

Forelli--Rudin construction and asymptotic expansion of Szegö kernel on Reinhardt domains

Miroslav Engliš and Hao Xu

Full-text: Open access

Abstract

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 Szegö kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szegö 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.

Article information

Source
Osaka J. Math. Volume 52, Number 4 (2015), 905-929.

Dates
First available in Project Euclid: 18 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1447856025

Mathematical Reviews number (MathSciNet)
MR3426621

Subjects
Primary: 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)

Citation

Engliš, Miroslav; Xu, Hao. Forelli--Rudin construction and asymptotic expansion of Szegö kernel on Reinhardt domains. Osaka J. Math. 52 (2015), no. 4, 905--929. https://projecteuclid.org/euclid.ojm/1447856025.


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