On Bernstein's Inequality and Kahane's Ultraflat Polynomials |
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Authors: | Herve Queffelec Bahman Saffari |
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Institution: | (1) URA 751, UFR de Mathematiques, Universite des Sciences et Techniques de Lille, 59655 Villeneuve d'Ascq Cedex, France;(2) URA 757 (Analyse Harmonique), Batiment 425, Mathematiques, Universite de Paris-Sud, 91405 Orsay, France |
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Abstract: | The investigation of
norm Bernstein inequalities
for polynomials with unimodular coefficients, leads to unexpected results. Some phenomena here upset our intuition. This
paper closely revisits the ultraflat polynomials whose existence was conjectured by Littlewood in 1966 and proved by Kahane
in 1980. A major role in this study is also played by arbitrary ultraflat polynomials, that is, including those that are
not necessarily obtained by variations or refinements of Kahane's method. |
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Keywords: | |
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