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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 and uniqueness of interpolatory polynomials of degree ≤ 2n-1 when their values and second derivatives are prescribed on n given nodes. Around this kind of interpolation - aptly termed (0, 2) interpolation - considerable literature has grown up since then. For more complete bibliography on this subject we refer 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 of the first kind (Tn(x) = cos n θ, x = cos θ).

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 Doctoral Fellowship Department of Mathematics, University of Alberta (1966) and from N.R.C. Grant M.C.A.-26(1964).

References

1. Bal, J.ázs and Turán, P., Notes on interpolation II. Acta Math. Acad. Sci. Hung. vol. 8 (1955), 201-215.Google Scholar
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4. Dzyadyk, V. K., Constructive characterization of functions satisfying the conditions Lip α(0 < α<1) on a finite segment of the realaxis. Izv. Akad. Nauk. SSSR. Ser. Mat. 20 (1955) 623-642.Google Scholar
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