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 , which are characterized by the property for . The index of such a function, counting the zeros of the polynomial in the right half-plane , 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.