Hermite and Hermite-Fejer Interpolation and Associated Product Integration Rules on the Real Line: The L 1 Theory

Lubinsky, D. S. ; Rabinowitz, P.

Canadian journal of mathematics, Tome 44 (1992) no. 3, pp. 561-590

Résumé

We investigate convergence in a weighted L 1 -norm of Hermite-Fejér and Hermite interpolation at the zeros of orthogonal polynomials associated with weights on the real line. The results are then applied to convergences of product integration rules. From the point of view of orthogonal polynomials, the new feature is that Freud and Erdös weights are treated simultaneously and that relatively few assumptions are placed on the weight. From the point of view of product integration, the rules exhibit convergence for highly oscillatory kernels (for example) and for functions of rapid growth at infinity.

Détail

DOI : 10.4153/CJM-1992-036-2

Mots-clés : 41A05, 65D05, 65D30, 42C05, Hermite-Fejér, Hermite, interpolation, product integration, convergence, infinite intervals, Freud weights, Erdös weights

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