Sharp Markov-type Inequalities for Rational Functions on Several Intervals

TL;DR

This paper establishes precise Rusak- and Markov-type inequalities for rational functions defined on multiple intervals, especially when these functions are large in the gaps, by analyzing their inverse images.

Contribution

It introduces sharp inequalities for rational functions on several intervals, extending classical results to more complex domain configurations.

Findings

Derived sharp Rusak- and Markov-type inequalities for rational functions

Extended inequalities to functions large in gaps on multiple intervals

Analyzed inverse images of intervals for inequality bounds

Abstract

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.