arXiv subjects

Álvaro González Cortés

Publications and source records attributed to Álvaro González Cortés.

2 recordsLinked to original sources

arXiv2026

Diagonalization of nonlinear functions in finite-dimensional spaces and the case of $\mathbb R^2$

This paper introduces a new theoretical framework for the diagonalization of nonlinear functions defined in finite-dimensional real Euclidean spaces. Extending classical results from linear algebra, we provide a unified setting to determine when a nonlinear map can be represented in diagonal form via a change of basis. Due to the complexity of the equations involved, the final part of the paper focuses primarily on the two-dimensional case, for which clear characterizations can be obtained. We also illustrate how these theoretical findings can be applied to classical contexts, such as differential equations, dynamical systems, and the explicit computation of higher-order compositions and inverses of functions.

math.FA↗

arXiv2026

Analytic integration of metric-valued functions in Lipschitz free spaces

We develop an integration theory for functions taking values in a metric space. Following a Bochner-type construction, we define the concept of free integral as an element of the Lipschitz-free space $\mathcal{F}(M)$. We establish the main properties of this integral, including duality formulas, and the study of the resulting space of free integrable functions. We also cover when the metric space is a Banach space: in this setting, the free integral has an interpretable decomposition generalising the Bochner integral. We then connect the free integral with the geometry of $\mathcal{F}(M)$ by showing that it always produces convex integrals of molecules. This allows to study extremal properties within the unit ball of $\mathcal{F}(M)$. Finally, we provide a detailed example to illustrate the framework we develop.

math.FA↗