  Scalar rational functions with a non-negative real part on the right half
plane, called positive, are classical in the study of electrical networks,
dissipative systems, Nevanlinna-Pick interpolation and other areas. We here
study generalized positive functions, i.e with a non-negative real part on the
imaginary axis. These functions form a Convex Invertible Cone, cic in short,
and we explore two partitionings of this set: (i) into a pair of even and odd
subcics and (ii) to (infinitely many non-invertible) convex cones of functions
with prescribed poles and zeroes in the right half plane. It is then shown that
a positive function can always be written as a sum of even and odd part, only
over the larger set of generalized positive. It is well known that over
positive functions Nevanlinna-Pick interpolation is not always feasible. Over
generalized positive, there is no easy way to carry out this interpolation. The
second partitioning is subsequently exploited to introduce a simple procedure
for Nevanlinna-Pick interpolation. Finally we show that only some of these
properties are carried over to generalized bounded functions, mapping the
imaginary axis to the unit disk.
