# Henkin measures for the Drury-Arveson space

## TL;DR

This paper demonstrates that certain Borel probability measures on the unit sphere in complex space are Henkin for the Drury-Arveson space's multiplier algebra but not in the classical sense, disproving a previous conjecture.

## Contribution

It provides the first example of measures that are Henkin for the multiplier algebra yet not classical Henkin, answering a conjecture negatively.

## Key findings

- Existence of measures that are Henkin for the multiplier algebra but not classically
- Disproof of Clouatre and Davidson's conjecture
- Insight into the structure of Henkin measures in complex analysis

## Abstract

We exhibit Borel probability measures on the unit sphere in $\mathbb C^d$ for $d \ge 2$ which are Henkin for the multiplier algebra of the Drury-Arveson space, but not Henkin in the classical sense. This provides a negative answer to a conjecture of Clou\^atre and Davidson.