2023•International Journal of MathematicsOpen access

The reduced Bergman kernel and its properties

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

Abstract

In this paper, we study some properties of the nth-order weighted reduced Bergman kernels for planar domains, [Formula: see text]. Specifically, we look at Ramadanov type theorems, localization, and boundary behavior 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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Key concepts: Mathematics, Bergman kernel, Kernel (algebra), Boundary (topology), Pure mathematics, Order (exchange), Type (biology), Transformation (genetics)