Cyclicity of Multipliers on the Unit Ball of C^n: A Corona-Based Approach

par Pouriya Torkinejad-Ziarati (IMT - Université de Toulouse)

lundi 20 oct. 2025, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

We study the cyclicity of multipliers in Dirichlet-type spaces D_\alpha(\mathbb{B}_n). Specifically, we show that a multiplier f analytic on a neighborhood of the closed unit ball, whose zero set on the unit sphere is a compact, smooth, complex tangential submanifold of real dimension m \leq n - 1, is cyclic in D_\alpha(\mathbb{B}_n) if and only if \alpha \leq \frac{2n - m}{2}, where m is the real dimension of the zero set of f on the boundary. Our approach combines classical results on peak sets in A^\infty(\mathbb{B}_n) due to Chaumat and Chollet with a Corona-type theorem with two generators for the multiplier algebra.