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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
##### Keywords:
power series; $$n$$-circular bounded domain; Bohr theorem
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