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This article is cited in 27 scientific papers (total in 27 papers)
Contour and solid structure properties of holomorphic functions of a complex variable
P. M. Tamrazov
Abstract:
For a $f$ function holomorphic in an open set $G$ the paper solves problems on the relationships between its properties along $\partial G$, the boundary of $G$, on the one hand and along $\overline G$, the closure of $G$, on the other. The properties discussed are those that can be expressed in terms of the derivatives, moduli of continuity, and rates of decrease or increase of the function along $\overline G$ and along $\partial G$. The results are established for very wide classes of sets $G$ and majorants of the moduli of continuity. In particular, all the main results are true for every bounded simply-connected domain and any majorant of the type of a modulus of continuity. A number of problems posed in 1942 by Sewell are solved.
Received: 10.01.1972
Citation:
P. M. Tamrazov, “Contour and solid structure properties of holomorphic functions of a complex variable”, Russian Math. Surveys, 28:1 (1973), 141–173
Linking options:
https://www.mathnet.ru/eng/rm4836https://doi.org/10.1070/RM1973v028n01ABEH001398 https://www.mathnet.ru/eng/rm/v28/i1/p131
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