A sequence of extremal problems for trigonometric polynomials (Q1122087)
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scientific article; zbMATH DE number 4105549
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sequence of extremal problems for trigonometric polynomials |
scientific article; zbMATH DE number 4105549 |
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A sequence of extremal problems for trigonometric polynomials (English)
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1988
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The paper deals with the sequence of extremal problems \(I_ n=\sup \{(2\pi)^{-1}\int^{2\pi}_{0}| p(\theta)|^ 2 d\theta /p\in P_ n\},\) where \(P_ n\) denotes the set of nonnegative trigonometric polynomials of degree \(\leq n\) having constant term 1. The authors show that \((n+1)C_ 1\leq I_ n\leq 1+(n+1)C_ 1,\) where \(C_ 1=0.686981293... \).
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extremal problems
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trigonometric polynomials
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