Sharpened polynomial approximation

Alan Greenwell Law and Ann L. McKerracher

Vol. 51 (1974), No. 2, 491–494

DOI: 10.2140/pjm.1974.51.491

Abstract

In 1951, W. Wolibner showed that a real continuous function on a closed interval can be uniformly approximated by a polynomial which interpolates at prescribed points and which has a uniform norm agreeing with the function’s. This fit can be sharpened to include matching of some relative extrema as well. The paper characterizes functions that permit Simultaneous Approximation and Interpolation which is Norm-Preserving and Extrema-Matching over the entire interval except, perhaps, for a subset of arbitrarily-small diameter.

Mathematical Subject Classification 2000

Primary: 41A10

Milestones

Received: 1 February 1973

Published: 1 April 1974