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We prove that if(    φ  n    )n  =  0   ∞   ,      φ  0   ≡  1   , is a basis in the space of entire functions of  d  complex variables,  d  ⩾ 1, then, for every compact  K  ⊂ ℂ  d  , there is a compact  K  1  ⊃  K  such that, for every entire function    f  =   ∑   n  =  0   ∞f  n    φ  n, we have∑   n  =  0   ∞|    f  n    |        sup   K    |    φ  n    |   ⩽    supK  1|  f  |. A similar assertion holds for bases in the space of global analytic functions on a Stein manifold with the Liouville Property.

Bohr property of bases in the space of entire functions and its generalizations