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An inequality for trigonometric polynomials


Author: Lawrence A. Harris
Journal: Proc. Amer. Math. Soc. 84 (1982), 155-156
MSC: Primary 26D05
DOI: https://doi.org/10.1090/S0002-9939-1982-0633298-4
MathSciNet review: 633298
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Abstract: Our purpose is to obtain in an elementary way a sharp estimate on the derivative of a trigonometric polynomial of degree $ \leqslant n$ at a point $ \theta $ when the trigonometric polynomial has a known bound at the Chebyshev points and at $ \theta $.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Boas, Entire functions, Academic Press, New York, 1954. MR 0068627 (16:914f)
  • [2] -, Inequalities for polynomials with a prescribed zero, Studies in Math. Anal. and Related Topics (D. Gilbarg and H. Solomon et al., Eds.), Stanford Univ. Press, Stanford, Calif., 1962. MR 0150269 (27:270)
  • [3] J. G. van der Corput and G. Schaake, Ungleichungen für Polynome und trigonometrische Polynome, Compositio Math. 2 (1935), 321-361. MR 1556921
  • [4] T. J. Rivlin, The Chebyshev polynomials, Wiley, New York, 1974. MR 0450850 (56:9142)
  • [5] W. W. Rogosinski, Some elementary inequalities for polynomials, Math. Gaz. 39 (1955), 7-12. MR 0071573 (17:149d)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0633298-4
Article copyright: © Copyright 1982 American Mathematical Society

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