  Dissipative systems can be described in terms of non-hermitian hamiltonians
H, whose left eigenvectors f^j and right eigenvectors f_j form a bi-orthogonal
system. Bi-orthogonal systems could suffer from two difficulties. (a) If the
eigenvectors do not span the whole space, then H can only be diagonalized to
blocks (the Jordan-block problem). (b) Normalization would not be possible and
many familiar-looking formulas would fail if (f^j,f_j) = 0 for some j (the
orthonormalization problem). Waves in open systems provide a well-founded
realization of a bi-orthogonal system, and it is shown that these two problems
can indeed occur and are both related to higher-order poles in the
frequency-domain Green's function. The resolution is then given by introducing
a generalized duality transformation involving extra basis vectors, whose time
evolution is modified by polynomials in the time t. One thus obtains a
nontrivial extension of the bi-orthogonal formalism for dissipative systems.
