Canonical kernels versus constructible kernels

TL;DR

This paper compares canonical and constructive reproducing kernels for holomorphic functions in complex spaces, establishing new relations and insights into their behavior on specific domains of finite type.

Contribution

It introduces new results linking canonical and constructive kernels on finite type domains, enhancing understanding of their interplay in complex analysis.

Findings

Established relations between canonical and constructive kernels

Proved a new result on kernel behavior on finite type domains

Enhanced understanding of kernel comparison in complex spaces

Abstract

We study both canonical reproducing kernels and constructive reproducing kernels for holomorphic functions in $\CC^1$ and $\CC^n$. We compare and contrast the two, and also develop important relations between the two types of kernels. We prove a new result about the relationship between these two kernels on certain domains of finite type.