On the decomposition of a positive real function into positive real summands

Analytic functions of one variable with positive real part in the right half-plane, assuming real values on the real positive half-axis, are called positive real functions. In the paper necessary and sufficient conditions for a positive real function to be a sum of two positive real functions are given. Further the structure of any positive real function $f$ is shown when written in the form $f=f_0+g+h$ where $f_0,g,h$ are positive real functions and $f_0$ has all the pure imaginary poles of the function $f$.