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Bohr’s power series theorem in several variables. (English) Zbl 0888.32001
Summary: Generalizing a classical one-variable theorem of Bohr, we show that if an \(n\)-variable power series has modulus less than 1 in the unit polydisc, then the sum of the moduli of the terms is less than 1 in the polydisc of radius \(1/(3 \sqrt n)\).

MSC:
32A05 Power series, series of functions of several complex variables
32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30-XX)
30B10 Power series (including lacunary series) in one complex variable
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