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The Reduced Bergman Kernel and its Properties

Published 11 Sep 2022 in math.CV | (2209.04850v3)

Abstract: In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms.

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