Results 171 to 180 of about 518,009 (229)

On Factorization of Trigonometric Polynomials

Integral Equations and Operator Theory, 2004
In the present paper, using only ideas from elementary operator theory, a new proof of the operator version of the Fejer-Riesz theorem is given, and some of the ramifications of the ideas of the proof are studied. Starting with a sketch of some basic results on Schur complements and factorization, some simpler proofs are given.
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Turan's Inequalities for Trigonometric Polynomials

Journal of the London Mathematical Society, 1996
We 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

2004
In 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, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delvos, Franz-Jürgen, Knoche, Ludger
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Automated proof of mixed trigonometric-polynomial inequalities

Journal of symbolic computation, 2020
Shiping Chen, Zhong Liu
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Positivity of trigonometric polynomials

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004
The 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, 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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On the Average Number of Real Zeros of a Random Trigonometric Polynomial

Journal of the Indian Society for Probability and Statistics, 2018
Bijayini Nayak
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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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Complex WKB method for the difference Schrödinger equation with the potential being a trigonometric polynomial

, 2018
A. Fedotov, E. Shchetka
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