Results 151 to 160 of about 41,706 (192)
Some of the next articles are maybe not open access.
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 ...
openaire +1 more source
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 ...
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
Minima of Trigonometric Polynomials
Bulletin of the London Mathematical Society, 1998Let \(00\) such that \[ -\min_{x\in (0,2\pi]} \sum^N_{k= 1} (\cos n_kx+ \sin n_kx)\geq c{N^{1/2}\over\log N}. \]
openaire +1 more source
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.
openaire +1 more source
Conjugate trigonometric polynomials
Mathematical Notes of the Academy of Sciences of the USSR, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Integral Norms of Trigonometric Polynomials
Mathematical Notes, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
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.
openaire +3 more sources
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 \([0, \infty)\).
openaire +1 more source