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Bohr’s power series theorem in several variables
Proceedings of the American Mathematical Society · 1997 · Vol. 125(10) · pp. 2975–2979
Harold P. Boas✉(Texas A&M University)Dmitry Khavinson(University of Arkansas at Fayetteville)
Abstract
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 $1/(3\sqrt n )$.
Polynomial and algebraic computationComputability, Logic, AI AlgorithmsAdvanced Algebra and LogicPolydiscPower seriesBohr modelMathematicsSeries (stratigraphy)Bohr radiusModuliUnit (ring theory)Variable (mathematics)RADIUS
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