Results 181 to 190 of about 2,105 (196)
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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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Analysis and Mathematical Physics, 2023
The paper investigates two types of real trigonometric polynomial equations: \[ A(\theta)y'=B_1(\theta)+B_n(\theta)y^n \] and \[ A(\theta)y^{n-1}y'=B_1(\theta)+B_n(\theta)y^n \] The authors focus on the first equation and demonstrate that when $n\geq 4$, it has a maximum of 3 real trigonometric polynomial solutions if $n$ is even and 5 real ...
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The paper investigates two types of real trigonometric polynomial equations: \[ A(\theta)y'=B_1(\theta)+B_n(\theta)y^n \] and \[ A(\theta)y^{n-1}y'=B_1(\theta)+B_n(\theta)y^n \] The authors focus on the first equation and demonstrate that when $n\geq 4$, it has a maximum of 3 real trigonometric polynomial solutions if $n$ is even and 5 real ...
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A Property of the Ratio of Trigonometric Polynomials
Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1964The purpose of this note is to give a simple and relatively brief proof that it is possible to "factor out" zeros common to the numerator and de? nominator of a ratio of trigonometric polynomials. This result is needed in the paper of Cheney and Loeb [1, Lemma 9] where a different and longer proof is given.
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Integral Norms of Trigonometric Polynomials
Mathematical Notes, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Trigonometric polynomials with simple roots
Information Processing Letters, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ukrainian Mathematical Journal, 2009
Summary: We study inequalities of the Turán type for trigonometric polynomials and conjugate trigonometric polynomials in the quasi-norm of \(L_0\) and derivatives of any order. We present expressions for constants in these inequalities and obtain double-sided estimates for them.
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Summary: We study inequalities of the Turán type for trigonometric polynomials and conjugate trigonometric polynomials in the quasi-norm of \(L_0\) and derivatives of any order. We present expressions for constants in these inequalities and obtain double-sided estimates for them.
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Random Sampling of Multivariate Trigonometric Polynomials
SIAM Journal on Mathematical Analysis, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gröchenig, Karlheinz, Bass, Richard
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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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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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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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