Inverse images of polynomial mappings and polynomials orthogonal on them.
Let \(T\) be a polynomial with complex coefficients. First, the author studies the inverse images of the real and imaginary axes under \(T\) in detail. Then for an arbitrary polynomial \(\rho\) and a sequence \((p_n)_{n\in \mathbb{N}}\) of orthogonal polynomials the orthogonality behaviour of the sequence of polynomials \((\rho (p_n \circ T))_{n\in \mathbb{N}}\) is investigated. In particular, necessary and sufficient conditions are given such that \((\rho (p_n \circ T))_{n\in \mathbb{N}}\) is a subsequence of polynomials orthogonal with respect to a positive measure supported on a compact subset of the real line.
scientific article; zbMATH DE number 1915250