Extremal Trigonometric Polynomials
Initializing live version

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Consider the trigonometric polynomial of degree
such that not all of the
and
are zero. Babenko's theorem (1984) states that the measure of the subset of
for which
is at least
. The unique extremal polynomial, positive exactly on the interval
and normalized so that
, is constructed and shown for small values of
.
Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
$FailedPermanent Citation