The polyharmonic Bergman space for the union of rotated unit balls

TL;DR

This paper investigates the polyharmonic Bergman space on the union of rotated unit balls, deriving explicit formulas for the kernels using zonal polyharmonics and extending results to weighted spaces.

Contribution

It introduces explicit kernel formulas for the polyharmonic Bergman space on rotated unions of balls and extends these to weighted spaces, advancing the understanding of these function spaces.

Findings

Derived formulas for the Bergman kernel using zonal polyharmonics

Extended kernel formulas to weighted polyharmonic Bergman spaces

Provided explicit representations for these kernels

Abstract

In the paper we consider the polyharmonic Bergman space for the union of the rotated unit Euclidean balls. Using so called zonal polyharmonics we derive the formulas for the kernel of this space. Moreover, we study the weighted polyharmonic Bergman space. By the same argument we get the Bergman kernel for this space.