Multidimensional analogues of Bohr's theorem on power series

الأصل · EN

Generalizing the classical result of Bohr, we show that if an n-variable power series converges in an 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*D, where r = 1 - (2/3)(1/n). This constant is near to the best one for the domain D = z: |z₁| +... + |zₙ| < 1.