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Extremal Trigonometric Polynomials

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Consider the trigonometric polynomial of degree such that not all of the and are zero. Babenko's theorem (1984) states that the measure of the subset of for which is at least . The unique extremal polynomial, positive exactly on the interval and normalized so that , is constructed and shown for small values of .

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA

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