arXiv subjects

Rafael B. Gonzalez

Publications and source records attributed to Rafael B. Gonzalez.

2 recordsLinked to original sources

arXiv2026

Global hypoellipticity for perturbations of complex vector fields on the torus

We apply Krönecker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present situations in which this set is a discrete enumerable (hence, meager) subset of the real line, and we also show that this set may be a dense $\mathcal{G}_δ$ subset of the complex numbers (hence, nonmeager), which produces a contrast to a known result stating that this set has null Lebesgue measure.

math.AP↗

arXiv2023

Existence and regularity of ultradifferentiable periodic solutions to certain vector fields

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the connectedness of certain sublevel sets, the dimension of the subspace generated by the imaginary part of the coefficients, and Diophantine conditions. In addition, we show that these properties are also linked to the regularity of the solutions. The results extend previous ones in Gevrey classes.

math.AP↗