Abstract
We study the problem when an infinite system of linear functional equations μ n (f) = b n for n ∈ N has a real analytic solution f on ω C R d for every right-hand side (b n ) n ∈ N ⊆ C and give a complete characterization of such sequences of analytic functionals (μ n ). We also show that every open set w C R d has a complex neighbourhood Ω C C d such that the positive answer is equivalent to the positive answer for the analogous question with solutions holomorphic on Ω.
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