Zero asymptotics of Laurent-type Orthogonal Polynomials.

  1. Hernández, M.B. 1
  2. Finkelshtein, A.M. 1
  1. 1 Universidad de La Habana
    info

    Universidad de La Habana

    La Habana, Cuba

    ROR https://ror.org/04204gr61

Revista:
Journal of Approximation Theory

ISSN: 0021-9045

Año de publicación: 1996

Volumen: 85

Número: 3

Páginas: 324-342

Tipo: Artículo

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DOI: 10.1006/JATH.1996.0046 SCOPUS: 2-s2.0-0030163289 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Approximation Theory

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

Let {hn(z)} be the sequence of polynomials, satisfying ∫+∞0 hm(x) hn(x) x-λn dp(x) = δmn, 0 ≤ m ≤ n, where λn ∈ [0, 2n], n ∈ N. For a wide class of weights dp(x) and under the assumption limn → ∞ λn/(2n) = θ∈ [0, 1], two descriptions of the zero asymptotics of {hn(z)} are obtained. Furthermore, their analogues for polynomials orthogonal on [-1, 1] with respect to varying weights are considered. These results continue the study begun in [3]. © 1996 Academic Press, Inc.