S. Charpentier

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math.CV2026

Simultaneous polynomial approximation in Beurling-Sobolev spaces via Blaschke products

Stéphane Charpentier, Nicolas Espoullier, Rachid Zarouf

Assuming that $ϕ (t) = o (t^{2})$ as $t \to 0$ , we establish a lemma on simultaneous polynomial approximation in Orlicz-Beurling-Sobolev spaces $ℓ_{a}^{ϕ}$ . These spaces, endowed with the L…

math.CV2025

New results on universal Taylor series via weighted polynomial approximation

Stéphane Charpentier, Konstantinos Maronikolakis

We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions o…

math.CV2025

Quantitative incomplete polynomial approximation and frequently universal Taylor series

Stéphane Charpentier, Konstantinos Maronikolakis

Let $(τ_{n})_{n}$ be a sequence of real numbers in $(1, + \infty)$ . Using potential theoretic methods, we prove quantitative results - Bernstein-Walsh type theorems - about uniform appro…