The Trigonometric Polynomial Like Bernstein Polynomial

Norming meshes by Bernstein-like inequalities

We show that finite-dimensional univariate function spaces satisfying a Bernstein-like inequality admit norming meshes. In particular, we determine meshes with “optimal” cardinality for trigonometric polynomials on subintervals of the period. As an application we discuss the construction of optimal bivariate polynomial meshes by arc blending. 2000 AMS subject classification: 26D05, 42A05, 65T40.

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

Markov-bernstein Type Inequality for Trigonometric Polynomials with Respect to Doubling Weights on [−ω, Ω]

Various important weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc. inequalities, have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most of the cases this minimal assumption is the doubling condition. Here, based on a recently proved Bernstein-type inequality by D.S. Lubinsky, we establ...

Bernstein and Markov type inequalities for trigonometric polynomials on general sets∗

Bernstein and Markov-type inequalities are discussed for the derivatives of trigonometric and algebraic polynomials on general subsets of the real axis and of the unit circle. It has recently been proven by A. Lukashov that the sharp Bernstein factor for trigonometric polynomials is the equilibrium density of the image of the set on the unit circle under the mapping t → e. In this paper Lukasho...

The Bernstein and Nikolsky inequalities for trigonometric polynomials