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Forelli-Rudin construction and asymptotic expansion of Szegő kernel on Reinhardt domains. (English) Zbl 1333.32005

Inspired by Stein’s and Fefferman’s questions on the relations between the Bergman and the Szegő kernels as well as their asymptotic expansions, the authors study the asymptotic expansion of the Bergman and Szegő kernels on Hartogs domains, using the Forelli-Rudin construction. In particular they obtain graph-theoretic closed formulas for the coefficients in their asymptotic expansions. In the case of complete Reinhardt domains, the formula obtained by the authors becomes quite explicit using Nakazawa’s hodograph transformation.

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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References:

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