An RKHS approach to the indefinite Schwarz-Pick inequality on the bidisk

TL;DR

This paper generalizes the indefinite Schwarz-Pick inequality on the bidisk using a novel approach that links complex geometry with the geometry of reproducing kernel Hilbert spaces.

Contribution

It introduces a new generalization of the Schwarz-Pick inequality leveraging the connection between complex geometry and RKHS.

Findings

Generalized Schwarz-Pick inequality for the bidisk

Established a link between complex geometry and RKHS

Extended previous work on indefinite inequalities

Abstract

In this short note, we will give a generalization of the indefinite Schwarz-Pick inequality due to Seto [8]. Our approach is based on a connection between complex geometry and the geometry of reproducing kernel Hilbert spaces, which was crucially used in our previous work [6].