Reproducing kernel functions and asymptotic expansions on Jordan-Kepler manifolds

TL;DR

This paper explores the complex geometry of Jordan-Kepler manifolds, analyzing reproducing kernels and asymptotic expansions of holomorphic function spaces in both flat and bounded cases.

Contribution

It introduces Hilbert spaces of holomorphic functions on these manifolds and derives their reproducing kernels' complete asymptotic expansions.

Findings

Asymptotic expansion of reproducing kernels obtained

Hilbert spaces of holomorphic functions characterized

Results apply to both flat and bounded Jordan-Kepler manifolds

Abstract

We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by radial measures, and find the complete asymptotic expansion of the corresponding reproducing kernels for K\"ahler potentials, both in the flat and bounded setting.