Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Measures Original Research Article

Strong asymptotics for the sequence of monic polynomialsQn(z), orthogonal with respect to the inner product(f, g)S=∫ f(x) g(x) dμ1(x)+λ ∫ f′(x) g′(x) dμ2(x), λ>0,withzoutside of the support of the measureμ2, is established under the additional assumption thatμ1andμ2form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the (square of) the norm (Qn, Qn)Sand of the zeros ofQnis obtained.