The full Markov-Newman inequality for Müntz polynomials on positive intervals

Authors:
David Benko, Tamás Erdélyi and József Szabados

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2385-2391

MSC (2000):
Primary 41A17; Secondary 30B10, 26D15

Published electronically:
February 26, 2003

MathSciNet review:
1974635

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Abstract | References | Similar Articles | Additional Information

Abstract: For a function defined on an interval let

The principal result of this paper is the following Markov-type inequality for Müntz polynomials.

**Theorem.**

*Let be an integer. Let be distinct real numbers. Let . Then*

where the supremum is taken for all (the span is the linear span over ).

**1.**Peter Borwein and Tamás Erdélyi,*Polynomials and polynomial inequalities*, Graduate Texts in Mathematics, vol. 161, Springer-Verlag, New York, 1995. MR**1367960****2.**Peter Borwein and Tamás Erdélyi,*Newman’s inequality for Müntz polynomials on positive intervals*, J. Approx. Theory**85**(1996), no. 2, 132–139. MR**1385812**, 10.1006/jath.1996.0034**3.**Tamás Erdélyi,*Markov- and Bernstein-type inequalities for Müntz polynomials and exponential sums in 𝐿_{𝑝}*, J. Approx. Theory**104**(2000), no. 1, 142–152. MR**1753516**, 10.1006/jath.1999.3437**4.**D. J. Newman,*Derivative bounds for Müntz polynomials*, J. Approximation Theory**18**(1976), no. 4, 360–362. MR**0430604****5.**Edward B. Saff and Richard S. Varga,*On lacunary incomplete polynomials*, Math. Z.**177**(1981), no. 3, 297–314. MR**618197**, 10.1007/BF01162064

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Additional Information

**David Benko**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843

Email:
benko@math.tamu.edu

**Tamás Erdélyi**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843

Email:
terdelyi@math.tamu.edu

**József Szabados**

Affiliation:
Alfréd Rényi Institute of Mathematics, P.O.B. 127, Budapest, Hungary, H-1364

Email:
szabados@renyi.hu

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06980-6

Keywords:
M\"{u}ntz polynomials,
exponential sums,
Markov-type inequality,
Newman's inequality

Received by editor(s):
March 2, 2002

Published electronically:
February 26, 2003

Additional Notes:
The second author’s research was supported, in part, by the NSF under Grant No. DMS-0070826

The third author’s research was supported by OTKA Grant No. T32872

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2003
American Mathematical Society