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Some inequalities for trigonometric polynomials

Part of: Approximations and expansions Harmonic analysis in one variable Inequalities

Published online by Cambridge University Press:  09 April 2009

Clément Frappier
Clément Frappier
Affiliation:
Département de Mathématiques et de StatistiqueUniversité de MontréalC.P. 6128, Succursale “A” Montréal, Québec H3C 3J7, Canada
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Abstract

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We obtain various refinements and generalizations of a classical inequality of S. N. Bernstein on trigonometric polynomials. Some of the results take into account the size of one or more of the coefficients of the trigonometric polynomial in question. The results are obtained using interpolation formulas.

MSC classification

Secondary: 26D05: Inequalities for trigonometric functions and polynomials 42A05: Trigonometric polynomials, inequalities, extremal problems 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 216 - 226
Copyright
Copyright © Australian Mathematical Society 1985

References

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