# A linear topological invariant for spaces of quasianalytic functions of Roumieu type

## TL;DR

This paper establishes a new linear topological invariant for spaces of quasianalytic ultradifferentiable functions of Roumieu type, extending previous results and solving an open problem in the field.

## Contribution

It proves that these function spaces satisfy the dual interpolation estimate for small theta without additional convexity or weight conditions, broadening the understanding of their topological properties.

## Key findings

- Spaces satisfy dual interpolation estimate for small theta
- Results hold for arbitrary open subsets of R^d
- Extends previous work by removing convexity and weight assumptions

## Abstract

We show that the spaces $\mathcal{E}_{\{\omega\}}(\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\omega$ is a quasianalytic weight function and $\Omega$ is an arbitrary open subset of $\mathbb{R}^d$. This result was previously shown by Bonet and Doma\'nski [2] under the additional assumptions that $\Omega$ is convex and $\omega$ satisfies the condition $(\alpha_1)$. In particular, our work solves Problem 9.7 in [1].