Global complexification of real analytic globally subanalytic functions (Q314393)

The paper concerns the question of extending a real analytic globally subanalytic function to a definable holomorphic function in o-minimal structures expanding the field of reals. The author proves that the o-minimal structure \({\mathbb{R}_{an}}\) has a global complexification. He also proves that both the o-minimal structures \({\mathbb{R}_W}\) and \({\mathbb{R}_{an, \exp}}\) have a unary global complexification (where \(W\) is a convergent Weierstraß system).