Zero Distribution of Orthogonal Polynomials in a Certain Discrete Sobolev Space

We study the zero distribution of the polynomials {SNn} which are orthogonal with respect to the discrete Sobolev inner product 〈 f, g 〉 = ∫∞0 ƒ(x) g(x) dψ(x) + Nf(r)(0) g(r)(0), where ψ is a distribution function, N ≥ 0, r ≥ 1. SNn has n real, simple zeros; at most one of them is outside (0, ∞). The location of these zeros is given in relation to the position of the zeros of some classical polynomials (i.e., polynomials with respect to an inner product with N = 0).