Asymptotic first boundary value problem for holomorphic functions of several complex variables

Abstract: (Jointly with M. Shirazi)

Let $M$ be a complex manifold endowed with a distance $d$ and let $U\subset M$ be an arbitrary Stein domain. Let $\mu$ be a regular Borel measure on $U,$ such that non-empty open sets of $U$ have positive $\mu$ measure and $\nu$ a regular Borel measure on $\partial U.$ Let $\psi$ be a Borel measurable function on $\partial U,$ whose restriction to some closed subset $S\subset\partial U$ is continuous. Then, 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 zero at $p$ relative to $U.$

complex variablesdynamical systems

Audience: researchers in the topic

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