High-power asymptotics of some weighted harmonic Bergman kernels

2016/01/14 by Engliš, Miroslav · 1 citation
#31B05 #32A36 #46E22 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.03716

Abstract

For~weights ρ which are either radial on the unit ball or depend only on the vertical coordinate on the upper half-space, we describe the asymptotic behaviour of the corresponding weighted harmonic Bergman kernels with respect to ρ^α as α→+∞. This can be compared to the analogous situation for the holomorphic case, which is of importance in the Berezin quantization as well as in complex geometry.

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• Moment kernels, nested defects, and Cuntz dilations

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