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An extension of the Grünwald–Marcinkiewicz interpolation theorem

Published online by Cambridge University Press:  17 April 2009

T. M. Mills  and
P. Vértesi
T. M. Mills
Affiliation:
Department of Mathematics, La Trobe University, PO Box 199, Bendigo Vic. 3552, Australia
P. Vértesi
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, PO Box 127, Budapest H-1364, Hungary
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Abstract

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Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 299 - 320
Copyright
Copyright © Australian Mathematical Society 2001

References

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