Generalization of Benstein-Erdos Conjecture and the Lebesgue Function
University of South Alabama Analysis Seminar
Mobile, AL, USA
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.
Benstein-Erdos conjecture, Lebesgue function, polynomial norm inequalities
Analysis | Mathematics
Peter D. Dragnev (2010).
Generalization of Benstein-Erdos Conjecture and the Lebesgue Function. Presented at University of South Alabama Analysis Seminar, Mobile, AL, USA.