# Interpolating sequences in spaces with the complete Pick property

## TL;DR

This paper characterizes interpolating sequences in spaces with the complete Pick property, extending classical results and exploring pairs of Hilbert function spaces.

## Contribution

It provides a complete characterization of interpolating sequences for multiplier algebras in spaces with the complete Pick property, generalizing classical results.

## Key findings

- Interpolating sequences are characterized by separation and Carleson measure conditions.
- Generalization of Carleson's and Bishop-Marshall-Sundberg's results to broader spaces.
- Analysis of interpolating sequences for pairs of Hilbert function spaces.

## Abstract

We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.