On a polynomial inequality of E. J. Remez
HTML articles powered by AMS MathViewer
- by D. Dryanov and Q. I. Rahman PDF
- Proc. Amer. Math. Soc. 128 (2000), 1063-1070 Request permission
Abstract:
We prove a result which extends a well-known polynomial inequality of E. J. Remez and another one due to W. A. Markov.References
- B. Bojanov, Elementary Proof of the Remez Inequality, Amer. Math. Monthly 100 (1993), pp. 483–485.
- Peter Borwein and Tamás Erdélyi, Polynomials and polynomial inequalities, Graduate Texts in Mathematics, vol. 161, Springer-Verlag, New York, 1995. MR 1367960, DOI 10.1007/978-1-4612-0793-1
- G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971.
- Einar Hille, Analytic function theory. Vol. 1, Introductions to Higher Mathematics, Ginn and Company, Boston, 1959. MR 0107692
- V.A. Markov (W.A. Markov), Über polynôme die in einem gegebenem Intervalle möglichst wenig von Null abweichen, Math. Ann. 77 (1916), pp. 213–258.
- G. V. Milovanović, D. S. Mitrinović, and Th. M. Rassias, Topics in polynomials: extremal problems, inequalities, zeros, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. MR 1298187, DOI 10.1142/1284
- I. P. Natanson, Constructive function theory. Vol. I. Uniform approximation, Frederick Ungar Publishing Co., New York, 1964. Translated from the Russian by Alexis N. Obolensky. MR 0196340
- E.J. Remez, Sur une propriété des polynômes de Tchebycheff, Comm. Inst. Sci. Khar-kow 13 (1936), pp. 93–95.
- Theodore J. Rivlin, Chebyshev polynomials, 2nd ed., Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1990. From approximation theory to algebra and number theory. MR 1060735
Additional Information
- D. Dryanov
- Affiliation: Department of Mathematics, University of Sofia, James Boucher 5, 1126 Sofia, Bulgaria
- Email: dryanovd@fmi.uni-sofia.bg
- Q. I. Rahman
- Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada H3C 3J7
- Email: rahmanqi@ere.umontreal.ca
- Received by editor(s): May 12, 1997
- Received by editor(s) in revised form: May 25, 1998
- Published electronically: July 27, 1999
- Additional Notes: The first author was partially supported by the Bulgarian Ministry of Education, Sciences, and Technology through Contract 513/95.
- Communicated by: Frederick W. Gehring
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1063-1070
- MSC (1991): Primary 30A10, 30C10, 41A17
- DOI: https://doi.org/10.1090/S0002-9939-99-05092-3
- MathSciNet review: 1636946