Bulletin of the
Korean Mathematical Society BKMS

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

Keywords: Bergman kernel, transformation formula, quaternion variables, slice regular functions, slice Bergman kernel

MSC numbers: Primary 30G35; Secondary 32A25, 32A36