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Nonnegative Trigonometric Polynomials
Constructive Approximation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dimitrov, Dimitar K., Merlo, Clinton A.
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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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Biased Trigonometric Polynomials
The American Mathematical Monthly, 2007(2007). Biased Trigonometric Polynomials. The American Mathematical Monthly: Vol. 114, No. 9, pp. 804-809.
Hugh L. Montgomery +1 more
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Polynomials and Trigonometric Polynomials
1976Setting cos ϑ = x, the expressions $$ T_n \left( x \right) = \cos n\vartheta {\text{ }}U_n \left( x \right) = \frac{1} {{n + 1}}T'_{n + 1} \left( x \right) = \frac{{\sin \left( {n + 1} \right)\vartheta }} {{\sin \vartheta }}'{\text{ }}n = 0,1,2,...
George Pólya, Gabor Szegö
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Minima of Trigonometric Polynomials
Bulletin of the London Mathematical Society, 1998Let \(00\) such that \[ -\min_{x\in (0,2\pi]} \sum^N_{k= 1} (\cos n_kx+ \sin n_kx)\geq c{N^{1/2}\over\log N}. \]
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On Conjugate Trigonometric Polynomials
American Journal of Mathematics, 19431. In a joint paper with A. C. Schaeffer1 we discussed the following question: Let D be a closed domaina in the complex z-plane and z0 a fixed pointt of D. Let its consider all polynomtials f(z) of givez degree n forwhich f Jf(z) ? 1 in D and f(z0) is real.
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Conjugate trigonometric polynomials
Mathematical Notes of the Academy of Sciences of the USSR, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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On Factorization of Trigonometric Polynomials
Integral Equations and Operator Theory, 2004In 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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