An inequality for trigonometric polynomials
HTML articles powered by AMS MathViewer
- by Lawrence A. Harris PDF
- Proc. Amer. Math. Soc. 84 (1982), 155-156 Request permission
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
- Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
- R. P. Boas Jr., Inequalities for polynomials with a prescribed zero, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 42–47. MR 0150269
- J. G. Van der Corput and G. Schaake, Ungleichungen für Polynome und trigonometrische Polynome, Compositio Math. 2 (1935), 321–361 (German). MR 1556921
- Theodore J. Rivlin, The Chebyshev polynomials, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0450850
- W. W. Rogosinski, Some elementary inequalities for polynomials, Math. Gaz. 39 (1955), 7–12. MR 71573, DOI 10.2307/3611075
Additional Information
- © Copyright 1982 American Mathematical Society
- 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