The Polyharmonic Bergman Space for the Union of Rotated Unit Balls

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.2010 Mathematics Subject Classification. 31B30, 32A25, 32A36.