Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports

By Francisco Marcellán, J. J. M. Balcázar. 2006

54 citations recorded by the source corpus.

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we focus on the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some directions for future research are formulated.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4883ffd46bf1c6686619c36b3baa8edc434f8f46

Citations in the corpus

• On Sobolev orthogonal polynomials (2014, unknown): “For instance, in the case of symmetrically coherent Hermite case, that is, when either dμ0 = e −x(2) and dμ1 = 1 x2+ξ2 e −x(2) or dμ0 = x(2) + ξ2e−x 2 and dμ1 = e −x2, it holds, respectively, (1) lim n→∞ Sn(z,λ) Hn(z) = θ(λ) uniformly on compact subsets outside the real line; (2) lim n→∞ ⌊n2 ⌋1/2 Sn”