2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99786Let $Ω$ be a bounded, weakly pseudoconvex domain in C^n, n > 1, with real-analytic boundary. A real-analytic submanifold $M \subset bdΩ$ is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to $\Cal{O}(\barΩ)$. We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of $bdΩ$.Final version: corrected statement of Burns-Stout theorem and typos in Example 4.5; added Remark 1.5Complex Variables32A38, 32T25 (Primary) 32C25, 32D99 (Secondary)text