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 -