This article is cited in 1 paper

Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem

S. M. Ivashkovich


Abstract: The author proves that functions holomorphic in a neighborhood of the set $D+i\partial E$, where $D$ and $E$ are domains in $\mathbf R^2$, extend holomorphically to a neighborhood of the set $D_1+iE$, where $D_1$ is a subdomain of $D$. As a corollary he shows that functions analytic along $D+i\gamma$, where $\gamma$ is a curve in $\mathbf R^2$, are single-valued in a neighborhood of $D+i\gamma$ under certain restrictions to the size of $D$ and $\gamma$.
Bibliography: 4 titles.

UDC: 517.5

MSC: 32D10, 32A07

Received: 22.02.1980
Revised: 19.02.1981

 English version: Mathematics of the USSR-Izvestiya, 1982, 19:1, 189–196

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