Asymptotics of Sobolev orthogonal polynomials for symmetrically coherent pairs of measures with compact support

We study the strong asymptotics for the sequence of monic polynomials Q(n)(x), orthogonal 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 x outside of the support of the measure mu(2). We assume that mu(1) and mu(2) are symmetric and compactly supported measures on R satisfying a coherence condition. As a consequence, the asymptotic behaviour of (Q(n),Q(n))s and of the zeros of Q(n) is obtained.