S. Charpentier

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math.CV2026

Simultaneous polynomial approximation in Beurling-Sobolev spaces via Blaschke products

StÃ©phane Charpentier, Nicolas Espoullier, Rachid Zarouf

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

math.CV2025

New results on universal Taylor series via weighted polynomial approximation

StÃ©phane 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

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

math.CV2024

Bloch functions with wild boundary behaviour in $C^{N}$

We prove the existence of functions $f$ in the Bloch space of the unit ball $B_{N}$ of $C^{N}$ with the property that, given any measurable function $I ¨ $ on the unit…

Simultaneous polynomial approximation in Beurling-Sobolev spaces via Blaschke products

New results on universal Taylor series via weighted polynomial approximation

Quantitative incomplete polynomial approximation and frequently universal Taylor series

Bloch functions with wild boundary behaviour in CN

Bloch functions with wild boundary behaviour in $C^{N}$