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Inequalities for trigonometric polynomials

Approximation Theory and its Applications, 1997
Summary: Let \(t_n(x)\) be any real trigonometric polynomial of degree \(n\) such that \(\| t_n\|_\infty\leq 1\). Here, we are concerned with obtaining the best possible upper estimate of \[ \int^{2\pi}_0 | t^{(k)}_n(x)|^q dx\Biggl/\int^{2\pi}_0| t^{(k)}_n(x)|^{q- 2}dx, \] where \(q>2\).
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Two external problems for trigonometric polynomials

Sbornik: Mathematics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bounds for Trigonometric Polynomials

1976
Two methods for finding the maximum and minimum of a given trigonometric polynomial are described and studied. They are then applied to randomly generated polynomials. The resulting data suggest that one of the methods is superior to the other.
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Trigonometric Polynomials

2018
Dinh Dũng   +2 more
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Least Squares Trigonometric Polynomials

2014
Trigonometric polynomials, being linear in their parameters, come close to perfectly reproduce arbitrarily curved functions.
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Extremum Problems for Polynomials and Trigonometrical Polynomials

Journal of the London Mathematical Society, 1954
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