Alexey Lukashov

The order of Lebesgue constant of Lagrange interpolation on several intervals

We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain lower and upper estimates for the corresponding Lebesgue constant. The case of two intervals of equal lengths is simpler, and an explicit construction for two non-symmetric intervals will be given only in a special case.

Markov-type inequalities for rational functions on several intervals

In this paper, we give sharp Rusak- and Markov-type inequalities for rational functions on several intervals when the system of intervals is a \textquotedblleft rational function inverse image\textquotedblright\, of an interval and those functions are large in gaps.

Full length article: On trigonometric polynomials deviating least from zero on an interval

Extremal trigonometric polynomials with two fixed leading coefficients deviating least from zero on an interval shorter than the period are found. The complete solution splits into three different cases, one of them uses elliptic functions, and two others use only elementary functions.

Weighted Markov inequality on several intervals

In this study we give a weighted Markov inequality on several intervals.In this study we give a weighted Markov inequality on several intervals.

Weighted analogues of Bernstein-type inequalities on several intervals

We give weighted analogues of Bernstein-type inequalities for trigonometric polynomials and rational functions on several intervals.MSC:41A17, 42A05, 41A20.

Remez type inequality for trigonometric polynomials on an interval

In this study we give a Remez type inequality for trigonometric polynomials on an interval.