Description of extremal polynomials on several intervals and their computation. II (Q1307413)

The paper is a direct continuation of Part I (Acta Math. Hungar. 83, No. 1-2, 27-58 (1999; Zbl 0827.41015)]. Applications of the theory which was developed in Part I are given. Namely, complete description of minimal polynomials on two intervals, of Zolotarev, Richardson and Schur polynomials (i.e. minimal polynomials under different restrictions). Moreover a different approach is given to find systems of intervals (and even systems of intervals and arcs) such that the minimal polynomial for this system would be a \(T\)-polynomial. That approach gives an easy but very effective iterative algorithm for the computation of that \(T\)-polynomial. Finally, for two intervals it is demonstrated how to get \(T\)-polynomials with the help of Gröbner bases. Reviewer's remark: The case of two intervals (Theorems 3.1 and 5.4) was given by \textit{N. I. Achyeser} [Bull. Acad. Sci. URSS Cl. Sci. Math. Natur., 499-536 (1933; JFM 59.0995.02)]. It should be mentioned also that another type of algorithms for the computation of the minimal polynomials is given by \textit{V. I. Lebedev} [Russ. J. Numer. Anal. Math. Model. 8, No. 3, 195-222 (1993; Zbl 0818.65035), ibid. 8, No. 5, 397-426 (1993; Zbl 0818.65036)].