6 papers
The Fundamental Theorem of Calculus for Lebesgue-Stieltjes integrals involving non-monotonic derivators
Lamiae Maia, F. Adrián F. Tojo
In this work, we extend the concept of the Stieltjes derivative to encompass left-continuous derivators with bounded variation, thereby relaxing the monotonicity constraint. This g…
Constructive solutions of the heat equation with Stieltjes derivatives
Clara SenÃn, F. Adrián F. Tojo
In this work, we investigate the one-dimensional heat equation within the framework of Stieltjes calculus. We first consider the equation associated with two fixed derivators and d…
Stieltjes differential equations with bounded-variation derivators and application to thermal stress in solar panels
Lamiae Maia, F. Adrián F. Tojo
In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactn…
On the approximation properties of Stieltjes polynomials
VÃctor Cora, F. Adrián F. Tojo
We introduce and study the approximation properties of -polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case…
On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions
Francisco J. Fernández, Ignacio Márquez Albés, F. Adrián F. Tojo +1
We investigate the existence and uniqueness of solutions to first-order Stieltjes differential problems, focusing on the role of the Stieltjes derivative and its kernel. Unlike the…
Stieltjes differential systems with non monotonic derivators
Marlène Frigon, F. Adrián F. Tojo
In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of \emph{function of controlled…