  The construction of a class of unitary operators generating linear
superpositions of generalized coherent states from the ground state of a
quantum harmonic oscillator is reported. Such a construction, based on the
properties of a new ad hoc introduced set of hermitian operators, leads to the
definition of new basis in the oscillator Hilbert space, extending in a natural
way the displaced Fock states basis. The potential development of our method
and our results is briefly outlined.
