The first Zolotarev case in the Erdös-Szegö solution to a Markov-type extremal problem of Schur
DOI:
https://doi.org/10.24193/subbmath.2017.2.02Keywords:
Chebyshev, derivative, Erdös, extremal problem, inequality, Markov, polynomial, quartic, Schur, Shadrin, Szegö, ZolotarevAbstract
References
Achieser, N. I., Theory of Approximation, Dover Publications, Mineola N.Y., 2003 (Russian 1947).
Collins, G. E., Application of quantifier elimination to Solotareff´s approximation problem, in Stability Theory: Hurwitz Centenary Conference, (R. Jeltsch et al., eds.), Ascona 1995, Birkhäuser Verlag, Basel, 1996 (ISNM 121), 181-190.
Erdös, P., Szegö, G., On a problem of I. Schur, Ann. Math. 43 (1942), 451-470.
Finch, S. R., Zolotarev-Schur Constant, in Finch, S. R., Mathematical Constants, Cambridge University Press, Cambridge (UK), 2003, 229-231.
Grasegger, G., Vo, N. Th., An algebraic-geometric method for computing Zolotarev polynomials, Technical report no. 16-02, RISC Report Series, Johannes Kepler University, Linz, Austria, 2016, 1-17.
Lazard, D., Solving Kaltofen’s challenge on Zolotarev’s approximation problem, in Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), (J.-G. Dumas, ed.), Genova 2006, ACM, New York, 2006, 196-203.
Malyshev, V. A., The Abel equation, St. Petersburg Math. J. 13 (2002), 893-938 (Russian 2001).
Markov, A. A., On a question of D. I. Mendeleev, Zapiski. Imper. Akad. Nauk., St. Petersburg, 62 (1889), 1-24 (Russian). www.math.technion.ac.il/hat/fpapers/mar1.pdf
Markov, V. A., On functions deviating least from zero, Izdat. Akad. Nauk., St. Petersburg, 1892, iv + 111 (Russian). www.math.technion.ac.il/hat/fpapers/vmar.pdf
Milovanović, G. V., Mitrinović, D. S., Rassias, Th. M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
Peherstorfer, F., Schiefermayr, K., Description of extremal polynomials on several intervals and their computation. II, Acta Math. Hungar. 83 (1999), 59-83.
Rack, H.-J., On polynomials with largest coefficient sums, J. Approx. Theory 56 (1989), 348-359.
Rivlin, Th. J., Chebyshev Polynomials, 2nd ed., Wiley, New York, 1990.
Schur, I., Über das Maximum des absoluten Betrages eines Polynoms in einem gegebenen Intervall, Math. Z. 4 (1919), 271-287.
Shadrin, A., Twelve proofs of the Markov inequality, in Approximation Theory: A volume dedicated to Borislav Bojanov, (D. K. Dimitrov et al., eds.), M. Drinov Acad. Publ. House, Sofia, 2004, 233-298.
Shadrin, A., The Landau-Kolmogorov inequality revisited, Discrete Contin. Dyn. Syst. 34 (2014), 1183-1210.
Todd, J., A legacy from E. I. Zolotarev (1847-1878), Math. Intell. 10 (1988), 50-53.
Vlček, M., Unbehauen, R., Zolotarev polynomials and optimal FIR filters, IEEE Trans. Signal Process. 47 (1999), 717-730. Corrections: IEEE Trans. Signal Process. 48 (2000), 2171.
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