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On A Problem of P. Turán on Lacunary Interpolation*

Published online by Cambridge University Press:  20 November 2018

A. K. Varma
A. K. Varma*
Affiliation:
University of Alberta, Edmonton
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In 1955, Suranyi and P. Turán [8] considered the problem of existence anduniqueness of interpolatory polynomials of degree ≤ 2n-1 when their valuesand second derivatives are prescribed on n given nodes. Around this kind ofinterpolation - aptly termed (0, 2) interpolation - considerable literaturehas grown up since then. For more complete bibliography on this subject werefer to J. Balazs [3], Later we considered [10] the problem of modified (0,2) interpolation when 2 the abscissas are the zeros of (1-x2) Tn(x), where Tn(x) is the Tchebycheff polynomial ofthe first kind (Tn(x) = cos n θ, x = cos θ).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 531 - 557
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

**

I take this opportunity to express my thanks to Professor P. Turán (Budapest) and to Professor A. Sharma (Edmonton) for helpful suggestions as the paper progressed.

*

The author acknowledges financial support from Post DoctoralFellowship Department of Mathematics, University of Alberta (1966) andfrom N.R.C. Grant M.C.A.-26(1964).

References

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