Growth of polynomials
by
K.K. Dewan
Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, INDIA

In the early part of this century,de la Vallie Poussin raised the following question of best approximation: Is it possible to approximate polygonal lines by polynomials of degree n with an error of o(1/n) as n becomes large ? This question was answered in the negative by S.Bernstein. For this he proved and made considerable use of an inequality concerning the derivatives of polynomials. This inequality and the corresponding inequality for functions of exponential type have been the starting point of considerable literature in Aproximation Theory. In this talk we will discuss some of the research centered around these inequalities. Some new results will also be presented.

Date received: August 12, 2003