On the approximation properties of Stieltjes polynomials
Classical Analysis and ODEs
2025-07-08 v1
Abstract
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 where the derivator has finitely many discontinuities, we prove that the space of -polynomials is dense in the space of uniformly -continuous functions. This result establishes a Weierstrass-type approximation theorem within the framework of Stieltjes calculus. The characterization of the closure of the space of -polynomials in the general case, where the derivator may exhibit more complex behavior, remains an open and challenging problem, which we briefly discuss.
Cite
@article{arxiv.2507.05080,
title = {On the approximation properties of Stieltjes polynomials},
author = {Víctor Cora and F. Adrián F. Tojo},
journal= {arXiv preprint arXiv:2507.05080},
year = {2025}
}