Vol. 24, No. 1, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A persistent local maximum of the pth power deviation on an interval, p < 1

T. S. Motzkin and J. L. Walsh

Vol. 24 (1968), No. 1, 133–142
Abstract

The deviation of the polynomial p0(x) c from the given function f(x) ≡|x|1∕αsgx,p + α > 2,w(ixj) nonnegative, bounded, and integrable but not a null function, is defined as δ(c) 11w(x)|c f(x)|pdx, whence δ′′(0) < 0. Thus the error function c f(x) has a strong oscillation in the interval [–1, 1], yet δ(c) has a local maximum at c = 0 provided δ(0) = 0; this is true for every (allowable) choice of w(x). For suitably chosen w(x), the deviation δ(c) has a global maximum at c = 0,|c|1.

Mathematical Subject Classification
Primary: 41.30
Milestones
Received: 1 October 1965
Published: 1 January 1968
Authors
T. S. Motzkin
J. L. Walsh