Orthogonality of some sequences of the rational functions and the Müntz polynomials

In this paper we investigate the inner products in the space of rational functions and the space of Müntz polynomials. We prove that the orthogonality of a sequence in one of mentioned spaces can be induced by the orthogonality of the corresponding sequence in another space. Finally, we point to several special cases, i.e., some very different classes of well–known functions we represent on a unique way.