# The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces

## TL;DR

This paper investigates the surjectivity of the Borel map within r-ramification ultradifferentiable classes, providing new characterizations of quasianalyticity, extending previous results, and establishing a Whitney extension theorem in this context.

## Contribution

It extends the understanding of the Borel map's surjectivity in mixed ultradifferentiable classes and introduces a Whitney extension theorem for these spaces.

## Key findings

- Characterization of quasianalyticity in r-ramification ultradifferentiable classes
- Extension of Borel map image results to mixed ultradifferentiable settings
- A version of the Whitney extension theorem for these classes

## Abstract

We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity in such classes, extend the results of Schmets and Valdivia about the image of the Borel map in a mixed ultradifferentiable setting, and obtain a version of the Whitney extension theorem in this framework.