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

About the operator creating secondary polynomials