Pseudo-lossless functions with application to the problem of locating the zeros of a polynomial

This paper contains an investigation of the class of pseudolossless rational functions
F(p) = N(p)/D(p)
, which are characterized by the property
\Re F(p) = 0
for
\Re p = 0
. The index of such a function, counting the zeros of the polynomial
N(p)+ D(p)
in the right half-plane
\Re p > 0
, enjoys some very useful decomposition properties. It is shown how an appropriate index theory of pseudo-lossless functions provides a framework in which the most classical results concerning the problem of locating the zeros of a polynomial can be unified, simplified, and generalized.