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Polynomials with some Prescribed Zeros

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman and
Mohd. Ali Khan
Q. I. Rahman
Affiliation:
Department of Mathematics, University of Montreal
Mohd. Ali Khan
Affiliation:
Department of Chemistry, Regional Engineering College, Srinagar (India).
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In connection with various problems concerning polynomials

on the unit interval, the Tchebycheff polynomial

is known to play a very important role [11, problem 34].

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967, pp. 179 - 189
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Bernstein, S. N., Sur l'ordre de la meilleure approximation defonctions continues par des polynómes de degrèdonnè. Mèmoires de l′Acadèmie Royale de Belgique, (2). vol. 4 (1911), pages 1-103.Google Scholar
2. Bernstein, S. N., Leçonssur les propriètèsextrèmaleset lameilleure approximation des fonctionsanalytiquesd'une variablerèelle. Paris (1922).Google Scholar
3. Boas, R. P. Jr, Entire functions. Academic Press, New York, (1955).Google Scholar
4. Boas, R. P. Jr, Inequalities for polynomials with a prescribed zero. Studies in Mathematical Analysis and related topics (Essays in honour of George Pólya), Stanford University Press, Stanford (1966).Google Scholar
5. Boas, R. P. Jr, Periodic entire functions. American Math. Monthlyvol. 71 (1966), page 782.Google Scholar
6. van der Corput, J. G. and Schaake, G., Ungleichungen fur Polynóme und trigonometrische Polynóme. Compositio Mathematica, vol. 2 (1933), pages 321-361. Berichtigung zu: Ungleichungen fur Polynóme und trigonometrische Polynóme. CompositioMathematica. vol. 3 (1933), page 128.Google Scholar
7. Davis, P. J., Interpolation and approximation. Blaisdell Publishing Company (1966).Google Scholar
8. Fekete, M., Übereinen Satz des Herrn Serge Bernstein. Journal fur diereine und angewandte Mathematik. vol. 146 (1911), pages 88-94.Google Scholar
9. Hille, E., Szegö, G. and Tamarkin, J. D., On some generalizations of a theorem of A. Markoff. Duke Mathematical Journalvol. 3 (1933), pages 729-739.Google Scholar
10. Ibragimov, I. I., Extremal properties of entire functions of finite degree, (in Russian), Baku (1966).Google Scholar
11. D., Nicholas Kazarinoff, Analytic inequalities. Holt, Rinehart and Winston, New York (1966).Google Scholar
12. Kellogg, O. D., unbounded polynomials in several variables. Mathematische Zeitschriftvol. 27 (1922), pages 55-64.Google Scholar
13. Korevaar, J., An inequality for entire functions of exponential type. Nieuw Arch. Wiskunde (2) vol. 23 (1944), pages 55-62.Google Scholar
14. Rahman, Q. I. and Unni, K. R., Extremal problems and polynomials of least deviation. Scripta Mathematica vol. 27 (1966), pages 303-329.Google Scholar
15. Schur, I., Über das Maximum des absoluten Betrageseines Polynoms in einem gegebenen Intervall. Mathematische Zeitschrift vol. 4 (1911), pages 271-287.Google Scholar
16. Szegö, G., Über einen Satz des Herrn Serge Bernstein. Schriftencfer Konigsberger Gelehrten Gesellschaft vol. 5 (1922), pages 59-70.Google Scholar