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On the minimum modulus of trigonometric polynomials


Author: George Benke
Journal: Proc. Amer. Math. Soc. 114 (1992), 757-761
MSC: Primary 42A05; Secondary 30C10
DOI: https://doi.org/10.1090/S0002-9939-1992-1069683-5
MathSciNet review: 1069683
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Abstract: For all even integers $ N$ greater than 2, a trigonometric polynomial $ {f_N}(x) = \sum\nolimits_{k = - N}^{{N^2}} {{a_k}{e^{ikx}}} $ satisfying $ \vert{a_k}\vert\; \leq \;1$ and $ 0.47N \leq \vert{f_N}(x)\vert \leq N$ is constructed.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1069683-5
Keywords: Trigonometric polynomials, extremal problems, unimodular polynomials
Article copyright: © Copyright 1992 American Mathematical Society

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