ASYMPTOTICS OF SOBOLEV ORTHOGONAL POLYNOMIALS FOR COHERENT PAIRS OF MEASURES

Strong asymptotics for the sequence of monic polynomials Q(n)(z), orth ogonal with respect to the inner product (f,g)(s) = integral (f(x)g(x) d mu(1)(x) + lambda integral f'(x) g'(x) d mu(2)(x), lambda>0, with z outside of the support of the measure mu(2), is established under the additional assumption that mu(1) and mu(2) form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the ( square of) the norm (Q(n), Q(n))(s) and of the zeros of Q(n) is obtain ed. (C) 1998 Academic Press.