Results 201 to 210 of about 32,914 (238)
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Turan's Inequalities for Trigonometric Polynomials
Journal of the London Mathematical Society, 1996We present a technique for establishing inequalities of the form \[ c |f |_\infty \leq \int^{2 \pi}_0 \varphi \biggl (\bigl |f^{(k)} (t) \bigr |\biggr) dt \leq M |f |_\infty \] in the set of all trigonometric polynomials of order \(n\) which have only real zeros. The function \(\varphi\) is assumed to be convex and increasing on \([0, \infty)\).
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Polynomials, Rational Functions and Trigonometric Polynomials
2004In this chapter we want to illustrate the relevance of complex numbers in some elementary situations. After a brief discussion of the algebra of polynomials in Section 5.1, we prove the fundamental theorem of algebra and discuss solutions by radicals of algebraic equations in Section 5.2.
Mariano Giaquinta, Giuseppe Modica
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Lacunary Interpolation by Antiperiodic Trigonometric Polynomials
BIT Numerical Mathematics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delvos, Franz-Jürgen, Knoche, Ludger
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Positivity of trigonometric polynomials
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004The paper introduces a modification of the well-known sum-of-squares relaxation scheme for semi-algebraic programming by Shor based on replacing the ordinary polynomials by their trigonometric counterparts. It is shown that the new scheme has certain theoretical advantages over the classical one: in particular, a trigonometric polynomial is positive if
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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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