Abstract
Many authors have dealt with problems related to the symmetrization of sequences of orthogonal polynomials on a real line or on a unit circle. Particular aspects are treated for quadratic or cubic decompositions. In this paper, we present a technique that unifies the treatment of these topics for an arbitrary positive order of decomposition n by considering a more general definition of orthogonality. This technique is based on the decomposition with respect to the cyclic group of order n. The main theorem is applied to the orthogonality on ( n−1)-symmetric curves. Some particular cases are singled out. These results may be useful in studying Hermite–Padé approximations, vector continued fractions and dynamical systems.
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