Inverse images of polynomial mappings and polynomials orthogonal on them

Let T be a polynomial with complex coefficients. First, we study the inverse images of the real and imaginary axes under a polynomial mapping T in detail. Then for an arbitrary polynomial rho and a sequence (p(n)) of orthogonal polynomials the orthogonality behaviour of the sequence of polynomials (rho(p(n) o T))(nis an element ofN) is investigated. In particular necessary and sufficient conditions are given such that (rho(p(n) o T))(nis an element ofN) is a subsequence of polynomials orthogonal with respect to a positive measure supported on a compact subset of the real line. (C) 2002 Elsevier Science B.V. All rights reserved.