Antonio Carbone

collaborators

6 papers

math.CV2026

Reconstruction of a slice regular function from some of its real components

Cinzia Bisi, Antonio Carbone, Riccardo Ghiloni

A basic property of holomorphic functions $f : D \to C$ defined on domains $D$ of $C$ is that $f$ is uniquely determined by its real part up to an additive constant.…

math.AG2026

Differentiable approximation of continuous locally definable maps that preserves the image

Antonio Carbone

Recently, we showed that continuous definable maps defined on compact definable sets can be uniformly approximated by continuous definable maps of class $C^{p}$ without cha…

math.AG2026

Applications of the Nash double of a Nash manifold with corners

Antonio Carbone, José F. Fernando

In this work we study some properties and applications of Nash manifolds with corners. Our first main result shows how to `build' a Nash manifold with corners ${\mathcal Q}\subset{…

math.AG2026

Nash approximation of differentiable semialgebraic maps

Antonio Carbone, José F. Fernando

Let $T \subset R^{n}$ be a semialgebraic set and let $μ \geq 0$ be a non-negative integer. We say that $T$ is a {\em Nash $μ$ -approximation target space} (or a $({\mathcal N},μ)…

math.CV2025

Division algebras of slice-Nash functions

Cinzia Bisi, Antonio Carbone

The purpose of this paper is to introduce the notion of Nash functions in the context of slice regular functions of one quaternionic or octonionic variable. We begin with a detaile…

math.CV2025

Holomorphic functions with Nash real part

Antonio Carbone

In this paper we show that a holomorphic function, defined on an open subset $D$ of $C^{n}$ , is a complex Nash function if and only if its real part (or equivalently its ima…