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Hermite and Hermite-Fejer Interpolation and Associated Product Integration Rules on the Real Line: The L1 Theory

Published online by Cambridge University Press:  20 November 2018

D. S. Lubinsky  and
P. Rabinowitz
D. S. Lubinsky
Affiliation:
Department of Mathematics University of the WitwatersrandP.O. Wits 2050 Republic of South Africa
P. Rabinowitz
Affiliation:
Department of Applied Mathematics and Computer Science The Weizmann Institute of Science Rehovot76100, Israel
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Abstract

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We investigate convergence in a weighted L1 -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.

Keywords

41A0565D0565D3042C05Hermite-FejérHermiteinterpolationproduct integrationconvergenceinfinite intervalsFreud weightsErdös weights
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 3 , 01 June 1992 , pp. 561 - 590
Copyright
Copyright © Canadian Mathematical Society 1992

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