TY - JOUR

T1 - Multidimensional analogues of Bohr's theorem on power series

AU - Aizenberg, Lev

PY - 1999

Y1 - 1999

N2 - Generalizing the classical result of Bohr, we show that if an nvariable 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 modulii of the terms is less than 1 in the homothetic domain r = D, where (Formula Presented). This constant is near to the best one for the domain D = (z: z1 + … + zn 1).

AB - Generalizing the classical result of Bohr, we show that if an nvariable 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 modulii of the terms is less than 1 in the homothetic domain r = D, where (Formula Presented). This constant is near to the best one for the domain D = (z: z1 + … + zn 1).

UR - http://www.scopus.com/inward/record.url?scp=85009830314&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-99-05084-4

DO - 10.1090/S0002-9939-99-05084-4

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AN - SCOPUS:85009830314

SN - 0002-9939

VL - 128

SP - 1147

EP - 1155

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -