Title

Generalization of Benstein-Erdos Conjecture and the Lebesgue Function

Document Type

Presentation

Presentation Date

9-14-2010

Conference Name

University of South Alabama Analysis Seminar

Conference Location

Mobile, AL, USA

Peer Review

Invited

Abstract

The Lebesgue function arising from Lagrange polynomial interpolation is a classical topic in Approximation theory. A 40-year old conjecture by Bernstein and Erdos asked under what condition on the interpolation nodes will the function have minimal uniform norm. It was proved by Kilgore, and De Boor and Pinkus simultaneously in 1978. I will present a generalization of the Lebesgue function and the related conjecture and relevant results, as well as open problems.

Keywords

Benstein-Erdos conjecture, Lebesgue function, polynomial norm inequalities

Disciplines

Analysis | Mathematics

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