  The Hamiltonian reggeon acting in Bargmann space is non-Hermitian with
respect to the standard scalar product associated to Bargmann space. Hence the
question arises, whether the eigenfunctions by the finite norm condition form a
complete basis. The main new results of this article are the determination of
the boundary conditions for the eigenvalue problem associated to this
Hamiltonian and the proof of the completeness of the generalized
eigen-functions of this operator. This article also provides an explicit
integral form of the inverse of reggeon's operator on the negative imaginary
axis and we give some spectral properties of our operator.
