Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Jacobi type

摘要

Let {Sn}n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product(f,g)S=∫f(x)g(x)dψ0(x)+λ∫f′(x)g′(x)dψ1(x)where λ>0 and {dψ0,dψ1} is a so-called coherent pair with at least one of the measures dψ0 or dψ1 a Jacobi measure. We investigate the asymptotic behaviour of Sn(x), for n→+∞ and x fixed, x∈C⧹[−1,1] as well as x∈(−1,1).