Bi-orthogonality and zeros of transformed polynomials

摘要

Let D and E be two real intervals. We consider transformations that map polynomials with zeros in D into polynomials with zeros in E. A general technique for the derivation of such transformations is presented. It is based on identifying the transformation with a parametrised distribution φ (x, µ), x ∈ E, µ ∈ D, and forming the bi-orthogonal polynomial system with respect to φ. Several examples of such transformations are given.