New Bernstein Type Inequalities for Polynomials on Ellipses

Bernd Fischer; Roland Freund

doi:10.1080/17476939108814485

New Bernstein Type Inequalities for Polynomials on Ellipses

Bernd Fischer
, Roland Freund

Institut für Mathematik

Abstract

We derive new and sharp estimates for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. We also present some new results for approximation problems of this type.

Originalsprache	Englisch
Zeitschrift	Complex Variables, Theory and Application: An International Journal
Jahrgang	16
Ausgabenummer	4
Seiten (von - bis)	289-305
Seitenumfang	17
DOIs	https://doi.org/10.1080/17476939108814485
Publikationsstatus	Veröffentlicht - 18.05.1990

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10.1080/17476939108814485

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abstract = "We derive new and sharp estimates for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. We also present some new results for approximation problems of this type.",

author = "Bernd Fischer and Roland Freund",

year = "1990",

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AU - Freund, Roland

PY - 1990/5/18

Y1 - 1990/5/18

N2 - We derive new and sharp estimates for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. We also present some new results for approximation problems of this type.

AB - We derive new and sharp estimates for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. We also present some new results for approximation problems of this type.

U2 - 10.1080/17476939108814485

DO - 10.1080/17476939108814485

M3 - Journal articles

VL - 16

SP - 289

EP - 305

JO - Complex Variables, Theory and Application: An International Journal

JF - Complex Variables, Theory and Application: An International Journal

IS - 4

ER -

New Bernstein Type Inequalities for Polynomials on Ellipses

Abstract

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