  The space of entire functions which are integrable with respect to the
Gaussian weight, known also as the Fock space, is one of the preferred
functional Hilbert spaces for modelling and experimenting harmonic analysis,
quantum mechanics or spectral analysis phenomena. This space of entire
functions carries a three parameter family of canonical isometric involutions.
We characterize the linear differential operators acting on Fock space which
are complex symmetric with respect to these conjugations. In parallel, as a
basis of comparison, we discuss the structure of self-adjoint linear
differential operators. The computation of the point spectrum of some of these
operators is carried out in detail.
