High-power asymptotics of some weighted harmonic Bergman kernels

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• 作者：Miroslav Engli&scaron ; ^a ; ^b ; ¹ ; ^{englis@math.cas.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46E22 ; secondary ; 31B05 ; 32A36
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：271
• 期：5
• 页码：1243-1261
• 全文大小：370 K

文摘

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${\rho }^{\alpha }$ as α→+∞$\alpha \to +\infty$. 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.