Characterizing Model Spaces Among the Finite Dimensional RKHS with Pick Kernels

TL;DR

This paper characterizes finite dimensional RKHS with complete Pick kernels that are model spaces, using conditions related to multiplier solutions and conjugation operators, advancing understanding of their structure.

Contribution

It provides new characterizations of finite dimensional RKHS with complete Pick kernels as model spaces, linking multiplier solutions and conjugation operators.

Findings

Characterizations based on multiplier problem solutions

Conditions involving conjugation operators

Insights into the structure of finite dimensional RKHS

Abstract

We give several characterizations of those finite dimensional HSRK with complete Pick kernels which are model spaces. One characterization involves the size of the solution to a multiplier problem. Another involves having a conjugation operator which is compatible with the RKHS structure.