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On a polynomial inequality of E. J. Remez
Author(s):
D.
Dryanov;
Q.
I.
Rahman
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1063-1070.
MSC (1991):
Primary 30A10, 30C10, 41A17
Posted:
July 27, 1999
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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:
- 1.
- B. Bojanov, Elementary Proof of the Remez Inequality, Amer. Math. Monthly 100 (1993), pp. 1-99. CMP 93:11
- 2.
- P. Borwein & T. Erdélyi, Polynomials and Polynomial Inequalities, Springer - Verlag, 1995. MR 97e:41001
- 3.
- G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971.
- 4.
- E. Hille, Analytic Function Theory, vol. I, Blaisdel Publishing Company , New York, 1959. MR 21:6415
- 5.
- V.A. Markov (W.A. Markov), Über polynôme die in einem gegebenem Intervalle möglichst wenig von Null abweichen, Math. Ann. 77 (1916), pp. 1-99.
- 6.
- G. V. Milovanovi\'{c}, D. S. Mitrinovi\'{c}, Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, World Scientific, Singapore, 1994. MR 95m:30009
- 7.
- I.P. Natanson, Constructive Function Theory, vol. I, Frederick Ungar Publishing Co., Inc., New York, 1964. MR 33:4529a
- 8.
- E.J. Remez, Sur une propriété des polynômes de Tchebycheff, Comm. Inst. Sci. Khar-kow 13 (1936), pp. 1-99.
- 9.
- T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, 2nd ed., Wiley & Sons, New York, 1990.MR 92a:41016
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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
DOI:
10.1090/S0002-9939-99-05092-3
PII:
S 0002-9939(99)05092-3
Keywords:
Polynomials,
Markov's inequality,
Remez inequality
Received by editor(s):
May 12, 1997
Received by editor(s) in revised form:
May 25, 1998
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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