Inequalities concerning polynomials and trigonometric polynomials

Sharp Integral Inequalities for Trigonometric Polynomials

Sharp inequalities for linear operators in the set of trigonometric polyno-mials with respect to integral functionals Ê 2π 0 ϕ(|f (x)|) dx over the class of all functions ϕ defined, nonnegative, and nondecreasing on the semi-axis [0, ∞) are discussed. 1.1. Let P be the real number field R or the complex number field C depending on the situation. Let C 2π = C 2π (P) be the space of continuous 2π...

The Bernstein and Nikolsky inequalities for trigonometric polynomials

On the L2 Inequalities Involving Trigonometric Polynomials and Their Derivatives

In this note we study the upper bound of the integral f {tW(x))2w(x)dx Jo where t(x) is a trigonometric polynomial with real coefficients such that \\t\\ao < 1 and w(x) is a nonnegative function defined on [0, n]. When w{x) = sin; x , where j is a positive integer, we obtain the exact upper bound for the above integral.

Rearrangements of Trigonometric Series and Trigonometric Polynomials

Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...

Some New Inequalities for Trigonometric Polynomials with Special Coefficients

Some new inequalities for certain trigonometric polynomials with complex semiconvex and complex convex coefficients are given.