  We are studying here the classical operator creating secondary polynomials
associated with an orthogonal system for a continuous probability density
function on a real interval. We know it is possible with the coupling of
Stietjes Transforms to build an auxiliary measure also called secondary
measure, making associated polynomials orthogonal. One of the consequences of
this definition is the possibility to extend this operator to a function having
interesting isometric characters. Under some hypotheses, there appears in the
construction of the secondary measure a function having a privileged role which
we will develop here: we will call it the reducer which will enable us among
other kings to reverse the studied extension and to make its adjunct explicit.
We will also illustrate it, in the case of classical orthogonal polynomials
with a few results on the Fourier's coefficients of this reducer with different
numerical applications.
