# A multiplier algebra functional calculus

## TL;DR

This paper extends the classical functional calculus for single contractions to tuples of commuting operators using multiplier algebras on Hilbert function spaces in multiple variables.

## Contribution

It generalizes the Sz.-Nagy--Foias $H^{
olinebreak ext{infty}}(
olinebreak ext{D})$ calculus to multivariable settings with a broad class of multiplier algebras.

## Key findings

- Develops a new functional calculus for operator tuples
- Extends classical theory to multivariable and multiplier algebra contexts
- Provides a framework for analyzing multivariable operator theory

## Abstract

This paper generalizes the classical Sz.-Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots, T_d)$ of commuting bounded operators on a Hilbert space and replace $H^{\infty}(\mathbb{D})$ with a large class of multiplier algebras of Hilbert function spaces on the unit ball in $\mathbb C^d$.