Results 131 to 140 of about 31,688 (173)

Polynomials and Trigonometric Polynomials

1976
Setting 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, 1998
Let \(00\) 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, 1943
1. 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, 1990
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Integral Norms of Trigonometric Polynomials

Mathematical Notes, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

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.
openaire   +3 more sources

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 \([0, \infty)\).
openaire   +1 more source

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
openaire   +1 more source

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
openaire   +2 more sources

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
openaire   +1 more source