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Inequalities for trigonometric polynomials
Approximation Theory and its Applications, 1997Summary: 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, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bounds for Trigonometric Polynomials
1976Two 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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Least Squares Trigonometric Polynomials
2014Trigonometric polynomials, being linear in their parameters, come close to perfectly reproduce arbitrarily curved functions.
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Jensen polynomials for the Riemann zeta function and other sequences
Proceedings of the National Academy of Sciences of the United States of America, 2019Larry G Rolen
exaly
Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind
Applied Mathematics and Computation, 2011Qiu-Ming Luo
exaly
Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2011Satoru Odake
exaly