Asymptotic behaviour of orthogonal polynomials relative to measures with mass points

  1. Ruiz, F.J.
  2. Guadalupe Hernández, José Javier
  3. Varona Malumbres, Juan Luis
  4. Pérez, M.
Revista:
Mathematika

ISSN: 0025-5793

Año de publicación: 1993

Volumen: 40

Páginas: 331-344

Tipo: Artículo

DOI: 10.1112/S0025579300007099 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Mathematika

Repositorio institucional: lock_openAcceso abierto Editor lock_openAcceso abierto Postprint

Resumen

The authors find general expressions for the orthonormal polynomials and the kernels relative to measures on the real line of the form μ+Mδc, in terms of those of the measures dμ and (x−c)2δc. They use these relations to show that Nevai's class M(0,1) is closed under addition of a mass point, and obtain several bounds for the polynomials and kernels relative to a generalized Jacobi weight with a finite number of mass points. They point out that the main application of this kind of estimates would be in the study of the convergence of the Fourier series, which they propose to present in a forthcoming paper

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