Sobre el teorema de interpolación de Borel en espacios de Hilbert

Let X be a real Hilbert space. If A_o is a real number and A_m is a real symmetric and continuous m-form defined on X^m, m = 1, 2, ... , we construct a real function j on X of class C∞ such that f^(m) is bounded in the bounded sets of X, f^(m)(0) = Am, m = 0, 1, 2, ... , and f is analytic in X\{0}.