Seminars: P. M. Gauthier, Asymptotic first boundary value problem for holomorphic functions of several complex variables

SEMINARS


Seminar "Complex analysis in several variables" (Vitushkin Seminar) December 16, 2020 16:45, Moscow, online

Asymptotic first boundary value problem for holomorphic functions of several complex variables P. M. Gauthier Université de Montréal, Département de Mathématiques et de Statistique
Abstract: Theorem (with Mohammad Shirazi, McGill University). Let $M$ be a complex manifold endowed with a distance $d$ and a regular Borel measure $\mu$, such that non-empty open sets have positive measure. Let $U \subset M$ be an arbitrary Stein domain and $\psi\in \mathcal M(\partial U)$ an arbitrary Borel measurable function on the boundary $\partial U$, whose restriction to some closed subset $S\subset\partial U$ is continuous. Then, for an arbitrary regular $\sigma$-finite Borel measure $\nu$ on $\partial U$, there exists a holomorphic function $f$ on $U$, such that, for $\nu$-almost every $p\in\partial U$, and for every $p \in S$, $f(x) \to \psi(p)$, as $x \to p$ outside a set of $\mu$-density 0 at $p$ relative to $U$. Language: English Website: https://mi-ras-ru.zoom.us/j/6119310351?pwd=anpleGlnYVFXNEJnemRYZk5kMWNiQT09 ^* ID: 611 931 0351. Password: 5MAVBP.