Indefinite structure of the Bergman kernel on the open unit disk

TL;DR

This paper investigates the underlying indefinite structure of the Bergman kernel on the open unit disk, constructing related invariant distances, birational maps, and kernels to explore their interactions.

Contribution

It introduces a novel framework linking the Bergman kernel with invariant distances, birational maps, and indefinite kernels, revealing new structural insights.

Findings

Constructed an invariant distance from the Bergman kernel

Developed birational maps associated with the kernel

Analyzed interactions between the kernel, distance, and maps

Abstract

In this paper, we focus on an indefinite structure lying behind the Bergman kernel on the open unit disk. In particular, an invariant distance, birational maps and an indefinite kernel are constructed from the Bergman kernel, and we deal with their interaction.