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.
Revue:
Mathematika

ISSN: 0025-5793

Année de publication: 1993

Volumen: 40

Pages: 331-344

Type: Article

DOI: 10.1112/S0025579300007099 GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Mathematika

Dépôt institutionnel: lock_openAccès ouvert Editor lock_openAccès ouvert Postprint

Résumé

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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