On Chebyshev–Markov Rational Functions over Several Intervals

AbstractChebyshev–Markov rational functions are the solutions of the following extremal problemminc1, …, cn∈Rxn+c1xn−1+…+cnωn(x)C(k)withKbeing a compact subset of R andωn(x) being a fixed real polynomial of degree less thann, positive onK. A parametric representation of Chebyshev–Markov rational functions is found forK=[b1, b2]∪…∪[b2p−1, b2p], −∞<b1⩽b2<…<b2p−1⩽b2p<+∞ in terms of Schottky–Burnside automorphic functions