Infinite systems of linear equations for real analytic functions

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.