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Multidimensional Analogues of Bohr's Theorem on Power Series

Lev Aizenberg
Organization: Bar-Ilan University, Israel
Journal / Anthology

Year: 1998

Generalizing the classical result of Bohr, we show that if an n-variable power series converges in n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the moduli of the terms is less than 1 in the homothetic domain r dot-product D, where r equals 1 minus the nth root of 2/3.

*Mathematics > Calculus and Analysis > Series