Lower bounds for derivatives of polynomials and Remez type inequalities

Authors:
Tamás Erdélyi and Paul Nevai

Journal:
Trans. Amer. Math. Soc. **349** (1997), 4953-4972

MSC (1991):
Primary 33A65; Secondary 26C05, 42C05

DOI:
https://doi.org/10.1090/S0002-9947-97-01875-8

MathSciNet review:
1407486

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Abstract | References | Similar Articles | Additional Information

Abstract: P. Turán [*Über die Ableitung von Polynomen*, Comositio Math. **7** (1939), 89-95] proved that if all the zeros of a polynomial lie in the unit interval , then . Our goal is to study the feasibility of for sequences of polynomials whose zeros satisfy certain conditions, and to obtain lower bounds for derivatives of (generalized) polynomials and Remez type inequalities for generalized polynomials in various spaces.

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Additional Information

**Tamás Erdélyi**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368

Email:
terdelyi@math.tamu.edu

**Paul Nevai**

Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210-1174

Email:
nevai@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01875-8

Keywords:
Markov type inequalities,
Remez type inequalities,
Tur\'{a}n type inequalities,
derivatives,
algebraic polynomials,
trigonometric polynomials,
generalized polynomials

Received by editor(s):
April 20, 1996

Additional Notes:
This material is based upon work supported by the National Science Foundation under Grants No. DMS–9024901 (both authors) and No. DMS–940577 (P. N.).

Article copyright:
© Copyright 1997
American Mathematical Society