R. Delaubenfels et Fy. Yao, ENTIRE SOLUTIONS OF THE ABSTRACT CAUCHY-PROBLEM IN A HILBERT-SPACE, Proceedings of the American Mathematical Society, 123(11), 1995, pp. 3351-3356
We show that, whenever the linear operator A is symmetric and densely
defined, on a Hilbert space, then the abstract Cauchy problem d/dz u(z
) = A(u(z)) (z is an element of C), u(0) = x has an entire solution,
for all initial data x in the image of e(-<(A)over bar A>), which is
a dense set.