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Multidimensional analogues of Bohr’s theorem on power series. (English) Zbl 0948.32001
This paper is devoted to the generalization of the classical Bohr theorem for \(n\)-dimensional space. The author establishes that if the series \[ \sum_\alpha c_\alpha z^\alpha \] converges in \(n\)-circular bounded complete domain \(D\) and its sum has modulus less than 1, then \[ \sum_\alpha|c_\alpha z^\alpha |<1 \] in the domain \(rD\).
In the paper the estimates of the parameter \(r\) are given for some concrete domains.

MSC:
32A05 Power series, series of functions of several complex variables
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